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

    <schemaVersion>X0306</schemaVersion>

    <documentType>5</documentType>

    <periodOfReport>2014-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <form3HoldingsReported>0</form3HoldingsReported>

    <form4TransactionsReported>0</form4TransactionsReported>

    <issuer>
        <issuerCik>0000895930</issuerCik>
        <issuerName>AMSURG CORP</issuerName>
        <issuerTradingSymbol>AMSG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000903095</rptOwnerCik>
            <rptOwnerName>CIGARRAN THOMAS G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>701 COOL SPRINGS BOULEVARD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>FRANKLIN</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37067</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common stock</value>
            </securityTitle>
            <transactionCoding>
                <transactionFormType></transactionFormType>
            </transactionCoding>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>153933</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>5.250% Mandatory Convertible Preferred Stock, Series A-1</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-12-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value>L</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>107.88</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2017-07-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <footnoteId id="F1"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Company's 5.250% mandatory convertible preferred stock, Series A-1 (the &quot;Preferred Stock&quot;) will automatically convert on July 1, 2017. Holders of the Preferred Stock have the right to convert the Preferred Stock at any time prior to July 1, 2017 into shares of the Company's common stock. If the applicable market value of the Company's common stock is equal to or greater than $55.13, the fixed conversion rate will be 1.8141 shares of the Company's common stock per share of Preferred Stock, or a total of 1,814.1 shares of common stock. If the applicable market value of the Company's common stock is less than or equal to $45, the fixed conversion rate will be 2.2222 shares of the Company's common stock per share of Preferred Stock, or a total of 2,222.2 shares of common stock. If the applicable market value of the Company's common stock is more than $45.00 and less than $55.13, then the conversion rate will be equal to $100 divided by the applicable market value of the Company's stock</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Thomas G. Cigarran</signatureName>
        <signatureDate>2015-02-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
