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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-06-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000007431</issuerCik>
        <issuerName>ARMSTRONG WORLD INDUSTRIES INC</issuerName>
        <issuerTradingSymbol>AWI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001471798</rptOwnerCik>
            <rptOwnerName>Melville James Clinton</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O  ARMSTRONG WORLD INDUSTRIES, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>2500 COLUMBIA AVENUE</rptOwnerStreet2>
            <rptOwnerCity>LANCASTER</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>17603</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-06-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2171</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7062</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units granted under the 2008 Directors Stock Unit Plan, as amended.  The units vest (contingent upon the Director's continued service as of such date) on the earlier of (i) the one-year anniversary of the grant; (ii) the death or total and permanent disability of the Director; or (iii) the date of any Change in Control Event (as defined in the Plan). Vested units will be acquirable by the Director at the time of the termination of his service on the Issuer's Board of Directors.</footnote>
        <footnote id="F2">Includes vested and unvested units as well as units not yet acquirable by the Director. Under the terms of the 2008 Directors Stock Unit Plan, vested units are not acquirable by the Director until (i) for those restricted stock units granted prior to June 2011, six (6) months following the termination of his  service on the Issuer's Board of Directors, and, (ii) for those units granted during and after June 2011, at the time of the termination of his service on the Issuer's Board of Directors. Also includes 4229 Common Shares owned by the Reporting Person that are not subject to the vesting/acquisition conditions described above.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Christopher S. Parisi, Attorney-in-fact for James C. Melville</signatureName>
        <signatureDate>2012-06-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
