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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-02-11</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001207074</issuerCik>
        <issuerName>VIRTUSA CORP</issuerName>
        <issuerTradingSymbol>VRTU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001671237</rptOwnerCik>
            <rptOwnerName>Nearhos Barry R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O VIRTUSA CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>132 TURNPIKE ROAD</rptOwnerStreet2>
            <rptOwnerCity>SOUTHBOROUGH</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01772</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>
            </securityTitle>
            <transactionDate>
                <value>2021-02-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20029</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 reports securities disposed of pursuant to the terms of the Agreement and Plan of Merger, dated as of September 9, 2020 (the &quot;Merger Agreement&quot;), by and among Austin HoldCo Inc., Austin BidCo Inc. (&quot;Sub&quot;), and the Issuer, pursuant to which Sub merged with and into the Issuer (the &quot;Merger&quot;) effective as of February 11, 2021 (the &quot;Effective Time&quot;). At the Effective Time, each issued and outstanding share of common stock of the Issuer and each unvested restricted stock unit held by the reporting person was cancelled and converted into the right to receive $51.35 in cash without interest and net of any withholding of taxes thereon.</footnote>
        <footnote id="F2">Includes 5,980 unvested restricted stock units.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Paul D. Tutun, Attorney In Fact</signatureName>
        <signatureDate>2021-02-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
