<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0101</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-05-20</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0001156826</issuerCik>
        <issuerName>ARCHSTONE SMITH TRUST</issuerName>
        <issuerTradingSymbol>ASN</issuerTradingSymbol></issuer>
<reportingOwner>
<reportingOwnerId>
            <rptOwnerCik>0001136856</rptOwnerCik>
            <rptOwnerName>HOLMES NED S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>  </rptOwnerStreet1>
            <rptOwnerStreet2>  </rptOwnerStreet2>
            <rptOwnerCity>  </rptOwnerCity>
            <rptOwnerState>  </rptOwnerState>
            <rptOwnerZipCode>  </rptOwnerZipCode>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector>
<isOfficer>0</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>1</isOther>
<officerTitle></officerTitle>
<otherText>Trustee</otherText></reportingOwnerRelationship></reportingOwner>
<nonDerivativeSecurity>
<securityTitle>
<value>Common Shares of Beneficial Interest</value></securityTitle>
<transactionDate>
<value>2003-05-20</value></transactionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>A</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved></transactionCoding>
<transactionTimeliness>
<value></value></transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>2000</value></transactionShares>
<transactionValue>
<value>24.29</value></transactionValue>
<transactionAcquiredDisposedCode>
<value>A</value></transactionAcquiredDisposedCode></transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>19745</value>
<footnoteId id="F1"/></sharesOwnedFollowingTransaction></postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value></directOrIndirectOwnership>
<natureOfOwnership>
<value></value></natureOfOwnership></ownershipNature></nonDerivativeSecurity>
<footnotes>
<footnote id="F1">Total direct includes 7,745 units in Issuer&apos;s Deferred Compensation Plan and 4,000 Restricted Share Units issued pursuant to Issuer&apos;s Equity Plan for Outside Trustees, 2,000 of which were issued on 5/21/02 and vest 25% a year over 4 years, and 2,000 of which were issued on 5/j20/03 and vest 33.33% a year over 3 years.  Indirect total includes 4,000 shares held in family partnerships and 5,554 shares held in trust for children.</footnote></footnotes>
<ownerSignature>
<signatureName>Erin McMahon, Attorney-in-Fact on behalf of Ned Holmes</signatureName>
<signatureDate>2003-05-21</signatureDate></ownerSignature></ownershipDocument>


