<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-12-15</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000040533</issuerCik><issuerName>GENERAL DYNAMICS CORP</issuerName>        <issuerTradingSymbol>GD</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001207051</rptOwnerCik><rptOwnerName>JOHNSON JAY L</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>C/O GENERAL DYNAMICS CORPORATION</rptOwnerStreet1><rptOwnerStreet2>3190 FAIRVIEW PARK DRIVE</rptOwnerStreet2><rptOwnerCity>FALLS CHURCH</rptOwnerCity><rptOwnerState>VA</rptOwnerState><rptOwnerZipCode>22042</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock, $1.00 par value</value></securityTitle><transactionDate><value>2003-12-15</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>J</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>117.0000</value></transactionShares><transactionPricePerShare><value>85.1500</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>776.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">Reflects stock received in lieu of director fees in accordance with outside directors' compensation program.</footnote></footnotes><remarks>The reporting person also has 2,600 stock options, as previously reported.</remarks><ownerSignature><signatureName>Margaret N. House, by power of attorney</signatureName><signatureDate>2003-12-16</signatureDate></ownerSignature></ownershipDocument>

