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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-11-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000717954</issuerCik>
        <issuerName>UNIFIRST CORP</issuerName>
        <issuerTradingSymbol>UNF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001453910</rptOwnerCik>
            <rptOwnerName>Sintros Steven S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O UNIFIRST CORP</rptOwnerStreet1>
            <rptOwnerStreet2>68 JONSPIN ROAD</rptOwnerStreet2>
            <rptOwnerCity>WILMINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01887</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3222</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15569</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Appreciation Rights</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>195.55</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-11-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>7132</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-11-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock ($0.10 par value)</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7132</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7132</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units granted to Mr. Sintros under the UniFirst Corporation Amended and Restated 2010 Stock Option and Incentive Plan. Such restricted stock units vest 20% per year on each anniversary of the grant date with the first vesting occurring on November 19, 2021.</footnote>
        <footnote id="F2">Consists of (i) 4,327 shares of Common Stock owned by the reporting person, (ii) 3,421 restricted stock units that will vest in four remaining equal annual installments on November 27, 2020, November 27, 2021, November 27, 2022, and November 27, 2023, (iii) 1,815 restricted stock units that will vest in three remaining equal annual installments on December 14, 2020, December 14, 2021 and December 14, 2022, (iv) 2,784 restricted stock units that will vest in four remaining equal annual installments on October 29, 2021, October 29, 2022, October 29, 2023 and October 29, 2024 and (v) 3,222 restricted stock units that will vest in five equal annual installments on November 19, 2021, November 19, 2022, November 19, 2023, November 19, 2024 and November 19, 2025.</footnote>
        <footnote id="F3">This Stock Appreciation Right becomes vested and exercisable 20% per year on each anniversary of the grant date with the first vesting occurring on the first anniversary of the grant date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Steven S. Sintros</signatureName>
        <signatureDate>2020-11-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
