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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-09-06</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000790070</issuerCik>
        <issuerName>EMC CORP</issuerName>
        <issuerTradingSymbol>EMC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001189196</rptOwnerCik>
            <rptOwnerName>TEUBER WILLIAM J JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>EMC CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>176 SOUTH STREET</rptOwnerStreet2>
            <rptOwnerCity>HOPKINTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>01748</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Chairman</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-31</value>
            </transactionDate>
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                <transactionCode>G</transactionCode>
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            </transactionCoding>
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                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
            </transactionAmounts>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
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                </directOrIndirectOwnership>
                <natureOfOwnership>
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                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
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                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option Right To Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>26.80</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-09-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>31279</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2013-08-08</value>
                <footnoteId id="F5"/>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-08-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>31279</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option Right To Buy</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>26.80</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-09-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>23745</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2013-08-08</value>
                <footnoteId id="F5"/>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2022-08-08</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23745</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In connection with the merger (the &quot;Merger&quot;) of Universal Acquisition Co. with and into EMC Corporation on September 7, 2016, these shares were acquired pursuant to the automatic net exercise of stock options occurring immediately prior to 11:59 p.m., New York City time on September 6, 2016 (the &quot;Vesting Effective Time&quot;).</footnote>
        <footnote id="F2">Consists of shares withheld by EMC to satisfy the applicable exercise price upon exercise of options and associated tax withholding obligations related to the automatic net exercise of options immediately prior to the Vesting Effective Time described in footnote 1 above.</footnote>
        <footnote id="F3">Shares withheld by EMC to satisfy certain taxes payable in connection with the vesting of previously awarded restricted stock units.</footnote>
        <footnote id="F4">In connection with the Merger, at the effective time of the Merger, each outstanding share of EMC Corporation common stock beneficially owned by the reporting person was automatically canceled and converted into the right to receive (i) $24.05 in cash and (ii) 0.11146 of a share of Class V Common Stock of Dell Technologies Inc. (f/k/a Denali Holding Inc.).</footnote>
        <footnote id="F5">In connection with the merger (the &quot;Merger&quot;) of Universal Acquisition Co. with and into EMC Corporation on September 7, 2016, these stock options were automatically net exercised immediately prior to 11:59 p.m., New York City time on September 6, 2016 (the &quot;Vesting Effective Time&quot;).</footnote>
        <footnote id="F6">In connection with the Merger, 7,819 of these stock options were accelerated and became fully vested and exercisable on August 17, 2016.</footnote>
        <footnote id="F7">In connection with the Merger, 4,749 of these stock options were accelerated and became fully vested and exercisable on August 17, 2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Barbara E. Coluci, Attorney In Fact</signatureName>
        <signatureDate>2016-09-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
