<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-09-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000724606</issuerCik>
        <issuerName>PANERA BREAD CO</issuerName>
        <issuerTradingSymbol>PNRA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001244907</rptOwnerCik>
            <rptOwnerName>BORLAND MARK</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>6710 CLAYTON ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RICHMOND HEIGHTS</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>63117</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP,Chief Supply Chain Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Choice Award (Right to Restricted Shs or Stock Options)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5689</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2005-09-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2005-09-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>50.25</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2005-09-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5689</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <value>2011-09-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5689</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5689</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents disposition of Choice Award &quot;defined below&quot; by election under the award. Choice awards represented the right to elect restricted shares of Class A common stock, par value $0.0001 per share (&quot;Class A Common Stock&quot;), or options to purchase shares of Class A Common Stock granted on 9/1/2005 under the Company?s 2005 Long-Term Incentive Program (&quot;LTIP&quot;), the Company?s 1992 Equity Incentive Plan (&quot;1992 Plan&quot;) and the Company?s 2001 Employee, Director and Consultant Stock Option Plan (&quot;2001 Plan&quot;) under which the Reporting Person could elect, effective 9/15/05, an award in the form of (i) up to 1422 shares of restricted Class A Common Stock under the 1992 Plan or (ii) non-statutory stock options (&quot;Stock Options&quot;) to purchase up to 5689 shares of Class A Common Stock under the 2001 Plan, or a combination of restricted stock and non-statutory stock options (in 25% increments).</footnote>
        <footnote id="F2">The portion of the award elected to be in the form of stock options was for stock options to purchase a number of shares equal to four(4) times the number of shares of restricted stock that would have been awarded.  Effectiveness of Choice Awards were subject to the condition that the Reporting Person sign an acknowledgement (the &quot;Acknowledgment&quot;) that he or she agrees to a Confidential and Proprietary Information and Non-Competition Agreement, a Statement of Company Policy Regarding Securities Trades by Company Personnel, and a Business Conduct Standards Policy.</footnote>
        <footnote id="F3">Represents grant of Stock Options to purchase 5689 shares of Class A Common Stock pursuant to election under Choice Award.  The Stock Options vest over a five-year period from the date of grant, with 25% vesting on the second anniversary, and an additional 25% vesting on the third, fourth and fifth anniversaries. The options covered by the agreement will terminate six years from the date of the agreement, but will be subject to earlier termination as provided in the award agreement or in the 2001 Plan or the LTIP.  The terms of the Choice Awards are described in footnote (1).</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Mark E. Hood, Attorney in fact for Mark Borland</signatureName>
        <signatureDate>2005-09-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
