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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-01-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000914024</issuerCik>
        <issuerName>SHAW GROUP INC</issuerName>
        <issuerTradingSymbol>SGR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001064342</rptOwnerCik>
            <rptOwnerName>MCALISTER ALBERT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>330 CHURCH STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LAURENS</rptOwnerCity>
            <rptOwnerState>SC</rptOwnerState>
            <rptOwnerZipCode>29360</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 (phantom shares)</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2007-01-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1109</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>133603</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Employee Director Stock Option (Right to Buy)</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>33.83</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-01-30</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1109</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2008-01-30</value>
            </exerciseDate>
            <expirationDate>
                <value>2017-01-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1109</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1109</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Phantom shares and Stock options automatically awarded to each non-employee director pursuant to the Company's 2005 Non-Employee Director Stock Incentive Plan (&quot;2005 Director Plan&quot;) upon their election/re-election to the Company's Board of Directors.  This award of phantom shares is made with an effective grant date of January 30, 2007.  The phantom shares vest one year after the effective date of grant.</footnote>
        <footnote id="F2">Of the 133,603 beneficially owned by the reporting person, 96,830 shares are owned directly by reporting person, 7,900 shares are owned indirectly by a charitable remainder trust and 27,764 are owned indirectly by antoher trust.  The reporting persons' spouse owns separately a total of 1,000 shares.</footnote>
        <footnote id="F3">Stock options automatically awarded to each non-employee director pursuant to the Company's 2005 Non-Employee Director Stock Incentive Plan (&quot;2005 Director Plan&quot;) upon their election/re-election to the Company's Board of Directors.  This award of options is made with an effective grant date of January 30, 2007.  The stock options are fully exercisable one year after the effective date of grant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Albert D. McAlister</signatureName>
        <signatureDate>2007-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
