<?xml version="1.0"?><ownershipDocument><schemaVersion>X0101</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-05-12</periodOfReport><issuer><issuerCik>0000795665</issuerCik><issuerName>METAL MANAGEMENT INC</issuerName>        <issuerTradingSymbol>mtlm</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001214290</rptOwnerCik><rptOwnerName>COZZI ALBERT A</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>  </rptOwnerStreet1><rptOwnerStreet2>  </rptOwnerStreet2><rptOwnerCity>  </rptOwnerCity><rptOwnerState>  </rptOwnerState><rptOwnerZipCode>  </rptOwnerZipCode></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Chief Executive Officer</officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-05-12</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>15000</value></transactionShares><transactionValue><value>0</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>24137</value><footnoteId id="F4" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-05-20</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>5580</value></transactionShares><transactionValue><value>0</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>29717</value><footnoteId id="F4" /><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><footnotes><footnote id="F1">On May 12, 2003, the Board of Directors of Metal Management, Inc. awarded Albert A. Cozzi 15,000 shares of Metal Management, Inc. common stock for services to be rendered in fiscal 2004.  The shares vest in their entirety on March 31, 2004.</footnote><footnote id="F2">The Board of Directors of Metal Management, Inc. awarded a bonus to Albert A. Cozzi for fiscal 2003 performance.  The bonus was paid partially in common stock.  Albert A. Cozzi will receive 5,580 shares of common stock.  The shares will vest equally over three years beginning April 1, 2004 and on each annual anniversary therafter through April 1, 2006.</footnote><footnote id="F3">Since the date of Mr. Cozzi's last ownership report, he transfered 4,300 shares of Metal Management, Inc. common stock and warrants to purchase a total of 228,096 shares of Metal Management, Inc. common stock to his ex-wife pursuant to a domestic relations order.</footnote><footnote id="F4">Includes 4,836 shares of common stock indirectly held by a Corporation.</footnote></footnotes><ownerSignature><signatureName>/s/ Albert A. Cozzi</signatureName><signatureDate>2003-06-19</signatureDate></ownerSignature></ownershipDocument>

