<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-12-16</periodOfReport>
    <issuer>
        <issuerCik>0000350894</issuerCik>
        <issuerName>SEI CORP</issuerName>
        <issuerTradingSymbol>SEIC</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001191721</rptOwnerCik>
            <rptOwnerName>HEILIG KATHY</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE FREEDOM VALLEY DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>OAKS</rptOwnerCity>
            <rptOwnerState>PA</rptOwnerState>
            <rptOwnerZipCode>19456</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Controller/Senior Vice Preside</officerTitle></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>29.56</value></conversionOrExercisePrice><transactionDate><value>2003-12-16</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionAmounts><transactionShares><value>20000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2010-12-16</value></exerciseDate><expirationDate><value>2013-12-16</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>20000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>20000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership><natureOfOwnership><value/></natureOfOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes/><remarks>The option vests upon the earlier of the Issuer's attainment of specific levels of earnings per share or seven years from the date of the grant.  The option will expire on the ten year anniversary of the date of the grant.</remarks><ownerSignature><signatureName>Michelle Vaughn (Attorney-in-Fact)</signatureName><signatureDate>2003-12-17</signatureDate></ownerSignature></ownershipDocument>

