<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-11-02</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000815065</issuerCik>
        <issuerName>STERIS CORP</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001209524</rptOwnerCik>
            <rptOwnerName>KOSECOFF JACQUELINE B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 5960 HEISLEY ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MENTOR</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>44060</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>29785</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>9063</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote Below.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>27.68</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3387</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-07-27</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3387</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>34.17</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2744</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2018-07-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2744</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>28.08</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3609</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <value>2019-07-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3609</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>32.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3133</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2020-08-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3133</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>31.61</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3121</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2021-08-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3121</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>32.36</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3218</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F8"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F8"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-08-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3218</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>43.92</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4657</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F9"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F9"/>
            </exerciseDate>
            <expirationDate>
                <value>2023-08-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4657</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>51.53</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4584</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F10"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F10"/>
            </exerciseDate>
            <expirationDate>
                <value>2024-08-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4584</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Director Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>64.05</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4110</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F11"/>
            </exerciseDate>
            <expirationDate>
                <value>2025-08-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>4110</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Career Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F12"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2015-11-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2845</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F12"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F12"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares, No Par Value</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2845</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of STERIS Corporation (&quot;STERIS&quot;) disposed of pursuant to merger of a wholly-owned subsidiary of STERIS plc (&quot;New STERIS&quot;) with and into STERIS, with STERIS surviving the merger as a wholly-owned subsidiary of New STERIS (the &quot;Merger&quot;), in exchange for ordinary shares of New STERIS, which was consummated simultaneous with and conditioned on New STERIS' acquisition of Synergy Health plc by commencing a &quot;recommended offer&quot; under English law. At the effective time of the Merger, each STERIS common share was cancelled and converted into the right to receive one New STERIS ordinary share.</footnote>
        <footnote id="F2">These shares are held in a revocable family trust of the Reporting Person and the Reporting Person's spouse, as Co-Trustees.</footnote>
        <footnote id="F3">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 3,387 ordinary shares of New STERIS for $27.68 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F4">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 2,744 ordinary shares of New STERIS for $34.17 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F5">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 3,609 ordinary shares of New STERIS for $28.08 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F6">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 3,133 ordinary shares of New STERIS for $32.34 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F7">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 3,121 ordinary shares of New STERIS for $31.61 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F8">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 3,218 ordinary shares of New STERIS for $32.36 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F9">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 4,657 ordinary shares of New STERIS for $43.92 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F10">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 4,584 ordinary shares of New STERIS for $51.53 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F11">This option is fully vested. This option was assumed by New STERIS in the Merger and converted to an option to purchase 4,110 ordinary shares of New STERIS for $64.05 per share, subject to the same terms and conditions that were applicable to the original STERIS option.</footnote>
        <footnote id="F12">At the effective time of the Merger, each STERIS career restricted stock unit was cancelled and converted to a New STERIS career restricted stock unit, subject to the same terms and conditions that were applicable to the original STERIS career restricted stock unit.  These New STERIS career restricted stock units are fully vested and will be settled in New STERIS ordinary shares six months after the cessation of the Director's Board service.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Dennis P. Patton, Authorized Representative under Power of Attorney</signatureName>
        <signatureDate>2015-11-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
