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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-06-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000869487</issuerCik>
        <issuerName>TANDY BRANDS ACCESSORIES INC</issuerName>
        <issuerTradingSymbol>TBAC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001200436</rptOwnerCik>
            <rptOwnerName>RUNDELL C A JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>8200 SPRINGWOOD DRIVE, SUITE 230</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>IRVING</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75063</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2004-06-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>1988-08-08</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>1988-08-08</value>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3594</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The phantom stock units convert to shares of common stock on a one-for-one basis.</footnote>
        <footnote id="F2">The phantom stock units accrued under the Tandy Brands Accessories, Inc. 1995 Stock Deferral Plan for Non-Employee Directors because of a cash dividend payable to all stockholders of record at the close of business on June 30, 2004. Pursuant to the Tandy Brands Accessories, Inc. 1995 Stock Deferral Plan for Non-Employee Directors, phantom stock units are credited, based on the amount of the cash dividend and the closing price of the Issuer's common stock on the record date, to the reporting person's bookkeeping reserve account, which account is maintained by the Issuer.  The phantom stock units are to be settled in a single distribution made at such time specified by the reporting person provided that the designated payment date must be no earlier than twelve (12) months following the establishment of the affected phantom stock unit.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark J. Flaherty as attorney-in-fact for C.A. Rundell, Jr.</signatureName>
        <signatureDate>2004-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>

