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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-06-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000034408</issuerCik>
        <issuerName>FAMILY DOLLAR STORES INC</issuerName>
        <issuerTradingSymbol>FDO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001282797</rptOwnerCik>
            <rptOwnerName>WINSTON MARY A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P. O. BOX 1017</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Vice President - CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>67.50</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2012-06-05</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12120</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2014-06-05</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-06-04</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12120</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12120</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This option was granted on June 5, 2012, under the Family Dollar Stores, Inc. 2006 Incentive Plan, and no portion of the option may be exercised prior to June 5, 2014.  Thereafter, the option will vest in cumulative installments of not more than 40% of the number of shares subject to the option on June 5, 2014, 70% on June 5, 2015, and 100% on June 5, 2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Beth R. MacDonald, by Power of Attorney</signatureName>
        <signatureDate>2012-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
