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

    <documentType>4/A</documentType><periodOfReport>2003-08-27</periodOfReport><dateOfOriginalSubmission>2003-10-27</dateOfOriginalSubmission>
    <issuer>
        <issuerCik>0000350894</issuerCik>
        <issuerName>SEI CORP</issuerName>
        <issuerTradingSymbol>SEIC</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001101310</rptOwnerCik>
            <rptOwnerName>MCCARTHY KATHRYN</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>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>600</value><footnoteId id="F1"/></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership><natureOfOwnership><value/></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><footnotes><footnote id="F1">The Form 4 filings for a gift transfer of 225 shares of SEI Stock was inadvertently filed under Kathryn McCarthy's CIK number.  This Form 4 filing corrects Mr. McCarthy's holding to be 600 shares of SEI Stock.  The gift transfer of 225 shares of SEI Stock was actually made by Wayne Withrow not Ms. McCarthy and is now reflected on Mr. Withrow's Form 4 filings dated October 27, 2003.</footnote></footnotes><remarks/><ownerSignature><signatureName>MIchelle Vaughn (Attorney-in-Fact)</signatureName><signatureDate>2003-10-28</signatureDate></ownerSignature></ownershipDocument>

