<?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>0001019711</rptOwnerCik>
            <rptOwnerName>HEMMINGHAUS ROGER R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>15750 IH-10 WEST, SUITE 200</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN ANTONIO</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>78249</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>882</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.3146</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>882</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14749</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <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="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>27</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>1988-08-08</value>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>1988-08-08</value>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, $1.00 par value per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>27</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14776</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 during the quarterly period ended June 30, 2004. The phantom stock units were credited to the reporting person's bookkeeping reserve account, which account is maintained by the Issuer, on June 30, 2004 and are to be settled 12 months following the reporting person ceasing to be a member of the board of directors.</footnote>
        <footnote id="F3">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 12 months following the reporting person ceasing to be a member of the board of directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark J. Flaherty as attorney-in-fact for Roger R. Hemminghaus</signatureName>
        <signatureDate>2004-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>

