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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-09-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000890264</issuerCik>
        <issuerName>EXA CORP</issuerName>
        <issuerTradingSymbol>EXA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001029160</rptOwnerCik>
            <rptOwnerName>SOROS FUND MANAGEMENT LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>250 WEST 55TH STREET, 38TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000900203</rptOwnerCik>
            <rptOwnerName>SOROS GEORGE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>250 WEST 55TH STREET, 38TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001387524</rptOwnerCik>
            <rptOwnerName>SOROS ROBERT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>250 WEST 55TH STREET, 38TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.001 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>700</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.1514</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1731357</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.001 par value per share</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13419</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>16.6005</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1744776</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">These shares of common stock (the &quot;Shares&quot;) of Exa Corporation (the &quot;Issuer&quot;) were purchased for the account of Quantum Partners LP, a Cayman Islands exempted limited partnership (&quot;Quantum Partners&quot;).</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These Shares were purchased in multiple transactions at prices ranging from $16.13 to $16.16, inclusive. The reporting persons undertake to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of Shares purchased at each separate price within the ranges set forth in footnotes (2) and (4) to this Form 4.</footnote>
        <footnote id="F3">Soros Fund Management LLC (&quot;SFM LLC&quot;) serves as principal investment manager to Quantum Partners. As such, SFM LLC has been granted investment discretion over portfolio investments, including the Shares held for the account of Quantum Partners.  George Soros serves as Chairman and Manager of SFM LLC and Robert Soros serves as Manager of SFM LLC.</footnote>
        <footnote id="F4">The price reported in Column 4 is a weighted average price. These Shares were purchased in multiple transactions at prices ranging from $16.40 to $16.66, inclusive.</footnote>
    </footnotes>

    <remarks>The filing of this statement shall not be deemed an admission that any of the Reporting Persons are the beneficial owner of any securities not held directly for its account for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or otherwise.</remarks>

    <ownerSignature>
        <signatureName>/s/ Regan O'Neill, as Assistant General Counsel</signatureName>
        <signatureDate>2017-09-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Regan O'Neill, as Attorney-in-Fact for George Soros</signatureName>
        <signatureDate>2017-09-27</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Regan O'Neill, as Attorney-in-Fact for Robert Soros</signatureName>
        <signatureDate>2017-09-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
