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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-01-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001303645</rptOwnerCik>
            <rptOwnerName>Cohen Phillip L</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>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Appreciation Right</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>211.82</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-01-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2020-01-17</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-01-17</value>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock ($0.10 par value)</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This stock appreciation right is exercisable in full on the grant date (01/17/2020) and must be settled in stock at the time of exercise. The grant has an expiration date of the earlier of January 17, 2028 or the second anniversary of the date that the grantee ceases to be a member of the Board.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David Whitman, Attorney-in-Fact</signatureName>
        <signatureDate>2020-01-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
