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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2016-03-01</periodOfReport>

    <dateOfOriginalSubmission>2016-03-02</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001301031</issuerCik>
        <issuerName>Demandware Inc</issuerName>
        <issuerTradingSymbol>DWRE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001298669</rptOwnerCik>
            <rptOwnerName>Adams Timothy M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O DEMANDWARE, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5 WALL STREET</rptOwnerStreet2>
            <rptOwnerCity>BURLINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01803</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP &amp; Chief Financial Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1406</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>34.7096</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>50425</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This sale was effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person to satisfy reporting person's tax withholding obligation upon scheduled vesting of a restricted stock award.</footnote>
        <footnote id="F2">The price reported is the weighted average of the shares sold.  The shares were sold at varying prices in the range of $34.36 to $35.10.  The reporting person undertakes, upon the request of the staff of the Securities and Exchange Commission, the issuer or a security holder of the issuer, to provide full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F3">Includes 268 shares acquired under the Demandware, Inc. Employee Stock Purchase Plan on December 31, 2015.</footnote>
        <footnote id="F4">This Form 4/A is being filed to correct the amount of securities beneficially owned following reported transactions. The 268 shares acquired under the Demandware, Inc. Employee Stock Purchase Plan on December 31, 2015 were inadvertently subtracted from, rather than added to, the amount of securities beneficially owned following the reported transaction on the original Form 4.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kathleen B. Patton, Attorney-in-Fact for Timothy M. Adams</signatureName>
        <signatureDate>2016-03-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
