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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-03-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001108109</issuerCik>
        <issuerName>COMMUNITY HEALTH SYSTEMS INC</issuerName>
        <issuerTradingSymbol>CYH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001463791</rptOwnerCik>
            <rptOwnerName>Ely James S. III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4000 MERIDIAN BLVD</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>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5894</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>307193</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4990</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By E5 Investors LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5894</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5894</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11788</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>29268</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>6.15</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>29268</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>29268</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>34483</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34483</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>19296</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19296</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Units (SU)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15967.943</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15967.943</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The security converts to common stock on a one-to-one basis.</footnote>
        <footnote id="F2">The restricted stock units vest in 1/3 increments on the first, second and third anniversary date of the date of the grant. Upon vesting, the Reporting Person will be issued that number of shares of common stock of the Company.</footnote>
        <footnote id="F3">The restricted stock units vest in 1/3 increments on the first, second and third anniversary of the date of grant.  Based on the Reporting Person's prior deferral election pursuant to the terms of the award agreement, the Reporting Person will be issued that number of shares of common stock of the Company upon the Reporting Person's cessation as a director or upon a date specified by the Reporting Person.</footnote>
        <footnote id="F4">The Stock Units were accrued under the Company's Directors' Fees Deferral Plan in lieu of a portion of the Reporting Person's Director Fees and are settled 100% in the Company's common stock on the last business day of the calendar quarter following cessation as a director or upon a date specified by the Reporting Person.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christopher G. Cobb, Attorney in Fact for James S. Ely III</signatureName>
        <signatureDate>2023-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
