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

    <documentType>4</documentType>
<periodOfReport>2003-10-01</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000093859</issuerCik>
        <issuerName>STEAK &amp; SHAKE CO</issuerName>
        <issuerTradingSymbol>SNS</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001242862</rptOwnerCik>
            <rptOwnerName>GEIGER DUANE</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>36 S. PENNSYLVANIA</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 500</rptOwnerStreet2>
            <rptOwnerCity>INDIANAPOLIS</rptOwnerCity>
            <rptOwnerState>IN</rptOwnerState>
            <rptOwnerZipCode>46204</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector>
<isOfficer>1</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle>VP, Planning, MIS</officerTitle>
<otherText></otherText>
</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>4000</value>
</transactionShares>
<transactionPricePerShare>
<footnoteId id="F1"/>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>6000</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>I</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value>See Footnote</value>
<footnoteId id="F1"/>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
<nonDerivativeHolding>
<securityTitle>
<value>Common Stock</value>
</securityTitle>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>17529</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeHolding>
</nonDerivativeTable>
<footnotes>
<footnote id="F1">This transaction reflects the grant to Mr. Geiger of 4,000 shares of Company stock pursuant to the Company&#039;s Capital Appreciation Plan, an employee benefit plan approved by the shareholders pursuant to Rule 16(b)(3).</footnote>
</footnotes>
<remarks></remarks>
<ownerSignature>
<signatureName>David C. Milne, Attorney in Fact</signatureName>
<signatureDate>2003-10-09</signatureDate>
</ownerSignature>
</ownershipDocument>

