-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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<SEC-DOCUMENT>0001209191-08-035911.txt : 20080609
<SEC-HEADER>0001209191-08-035911.hdr.sgml : 20080609
<ACCEPTANCE-DATETIME>20080609145352
ACCESSION NUMBER:		0001209191-08-035911
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20080606
FILED AS OF DATE:		20080609
DATE AS OF CHANGE:		20080609

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			ARCH COAL INC
		CENTRAL INDEX KEY:			0001037676
		STANDARD INDUSTRIAL CLASSIFICATION:	BITUMINOUS COAL & LIGNITE SURFACE MINING [1221]
		IRS NUMBER:				430921172
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		CITY PLACE ONE STE 300
		STREET 2:		ARCH MINERAL CORP
		CITY:			ST LOUIS
		STATE:			MO
		ZIP:			63141
		BUSINESS PHONE:		3149942700

	MAIL ADDRESS:	
		STREET 1:		CITYPLACE ONE SUITE 300
		STREET 2:		ARCH MINERAL CORP
		CITY:			CREVE COEUR
		STATE:			MO
		ZIP:			63141

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	ARCH MINERAL CORP
		DATE OF NAME CHANGE:	19970411

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			FELDMAN SHEILA B
		CENTRAL INDEX KEY:			0001181625

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13105
		FILM NUMBER:		08887903

	BUSINESS ADDRESS:	
		STREET 1:		575 MARYVILLE CENTRE DR
		STREET 2:		P O BOX 66760
		CITY:			ST LOUIS
		STATE:			MO
		ZIP:			63166-6760
		BUSINESS PHONE:		3146741000
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-06-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001037676</issuerCik>
        <issuerName>ARCH COAL INC</issuerName>
        <issuerTradingSymbol>ACI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181625</rptOwnerCik>
            <rptOwnerName>FELDMAN SHEILA B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONECITYPLACE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ST. LOUIS</rptOwnerCity>
            <rptOwnerState>MO</rptOwnerState>
            <rptOwnerZipCode>63141</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP - Human Resources</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>8.72</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7068</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>73.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4068</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Options (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>8.72</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2013-02-03</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12334</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The reporting person received 60,000 stock options on February 3, 2003.  The stock options vested ratably over a three-year period as follows:  20,000 stock options vested on February 3, 2004; 20,000 stock options vested on February 3, 2005; 20,000 stock options vested on February 3, 2006.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gregory A. Billhartz, Attorney-in-Fact</signatureName>
        <signatureDate>2008-06-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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