<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-10-01</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000047111</issuerCik><issuerName>HERSHEY FOODS CORP</issuerName>        <issuerTradingSymbol>HSY</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001049372</rptOwnerCik><rptOwnerName>CAMPBELL ROBERT H</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>100 CRYSTAL A DRIVE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>HERSHEY</rptOwnerCity><rptOwnerState>PA</rptOwnerState><rptOwnerZipCode>17033</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</value></securityTitle><transactionDate><value>2003-10-01</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>136.986</value></transactionShares><transactionPricePerShare><value>73</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2730.9267</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">Includes 92.592 shares acquired on March 14, 2003, June 13, 2003, and September 15, 2003, pursuant to a Hershey Foods Dividend Reinvestment Plan.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Robert H. Campbell</signatureName><signatureDate>2003-10-01</signatureDate></ownerSignature></ownershipDocument>

