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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-12-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001000228</issuerCik>
        <issuerName>HENRY SCHEIN INC</issuerName>
        <issuerTradingSymbol>HSIC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001008413</rptOwnerCik>
            <rptOwnerName>BERGMAN STANLEY M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O HENRY SCHEIN, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>135 DURYEA ROAD</rptOwnerStreet2>
            <rptOwnerCity>MELVILLE</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>11747</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman, CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-12-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                <natureOfOwnership>
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                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
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        <nonDerivativeTransaction>
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                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
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                <natureOfOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
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                </natureOfOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
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            <transactionDate>
                <value>2014-12-09</value>
            </transactionDate>
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            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
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                <transactionPricePerShare>
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                </transactionPricePerShare>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                    <value>I</value>
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                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock, par value $0.01 per share</value>
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            <transactionDate>
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                <transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>562400</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F21"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-09-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>430</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>561970</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F22"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>992</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>560978</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F23"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>427</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>560551</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F24"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>560451</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                    <footnoteId id="F25"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-20</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F11"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>157932</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>66008</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Limited Liability Company</value>
                    <footnoteId id="F26"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4401</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By 401(k) Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reflects a weighted average of sales made at prices ranging from $136.05 to $136.66 per share.  The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F2">Represents (i) 610,321 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 1,120 shares held by Mrs. Bergman.</footnote>
        <footnote id="F3">The price reflects a weighted average of sales made at prices ranging from $136.09 to $136.67 per share. The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F4">Represents shares held by a limited liability company. Stanley M. Bergman and Marion Bergman, Mr. Bergman's wife, each have voting and dispositive power with respect to the shares held by the limited liability company.</footnote>
        <footnote id="F5">The price reflects a weighted average of sales made at prices ranging from $134.27 to $135.26 per share. The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F6">Represents (i) 597,025 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 1,120 shares held by Mrs. Bergman.</footnote>
        <footnote id="F7">The price reflects a weighted average of sales made at prices ranging from $135.27 to $135.70 per share. The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F8">Represents (i) 587,374 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 1,120 shares held by Mrs. Bergman.</footnote>
        <footnote id="F9">The price reflects a weighted average of sales made at prices ranging from $134.32 to $135.31 per share. The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F10">The price reflects a weighted average of sales made at prices ranging from $135.32 to $135.67 per share. The Reporting Person, upon request by the Securities and Exchange Commission staff, the issuer, or a security holder of the issuer, will provide full information regarding the number of shares sold at each separate price for this transaction.</footnote>
        <footnote id="F11">Gift, not applicable.</footnote>
        <footnote id="F12">Represents (i) 574,704 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 1,120 shares held by Mrs. Bergman. On March 17, 2014, Mr. Bergman transferred 14,282 shares to the Bergman Family Trust 2 which is refelected in the numbers in the preceding sentence.</footnote>
        <footnote id="F13">On March 20, 2014, the Bergman Family Trust 2 transferred 10,102 shares to Mr. Bergman which is refelected in the number in Column 5 of this line item.</footnote>
        <footnote id="F14">Represents (i) 574,704 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 366 shares held by Mrs. Bergman.</footnote>
        <footnote id="F15">Represents (i) 574,704 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 146 shares held by Mrs. Bergman.</footnote>
        <footnote id="F16">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 13,033 shares held by Mrs. Bergman. On June 23, 2014, the Bergman Family Trust 2010 Trust 2 transferred 14,365 shares to Mrs. Bergman which is reflected in the numbers in the preceding sentence.</footnote>
        <footnote id="F17">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 3,401 shares held by Mrs. Bergman.</footnote>
        <footnote id="F18">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 3,146 shares held by Mrs. Bergman.</footnote>
        <footnote id="F19">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 2,526 shares held by Mrs. Bergman.</footnote>
        <footnote id="F20">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 2,506 shares held by Mrs. Bergman.</footnote>
        <footnote id="F21">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 2,061 shares held by Mrs. Bergman.</footnote>
        <footnote id="F22">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 1,631 shares held by Mrs. Bergman.</footnote>
        <footnote id="F23">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 639 shares held by Mrs. Bergman.</footnote>
        <footnote id="F24">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 212 shares held by Mrs. Bergman.</footnote>
        <footnote id="F25">Represents (i) 560,339 shares held by the Bergman Family 2010 Trust 2, of which Marion Bergman, Stanley M. Bergman's wife, is a co-trustee and a beneficiary and (ii) 112 shares held by Mrs. Bergman.</footnote>
        <footnote id="F26">Represents shares held by a limited liability company. Stanley M. Bergman and Marion Bergman, Mr. Bergman's wife, each have voting and dispositive power with respect to the shares held by the limited liability company. On March 20, 2014, the Bergman Family Trust 2 transferred 16,850 shares to the limited liability company which is reflected in the number in Column 5 of this line item.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer Ferrero (as Attorney-in-Fact) for Stanley M. Bergman)</signatureName>
        <signatureDate>2014-12-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
