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Proc-Type: 2001,MIC-CLEAR
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<SEC-DOCUMENT>0001209191-06-065558.txt : 20061218
<SEC-HEADER>0001209191-06-065558.hdr.sgml : 20061218
<ACCEPTANCE-DATETIME>20061218172059
ACCESSION NUMBER:		0001209191-06-065558
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20061215
FILED AS OF DATE:		20061218
DATE AS OF CHANGE:		20061218

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:			BESTEN C HENRY JR
		CENTRAL INDEX KEY:			0001046078
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13105
		FILM NUMBER:		061284251

	BUSINESS ADDRESS:	
		STREET 1:		CITYPLACE ONE STE 300
		CITY:			ST LOUIS
		STATE:			MO
		ZIP:			63141
		BUSINESS PHONE:		3149942700
</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>2006-12-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001046078</rptOwnerCik>
            <rptOwnerName>BESTEN C HENRY JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE CITYPLACE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 300</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>Senior VP-Strategic Dev.</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2006-12-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.97</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>13</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7248</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of phantom stock represents a right to receive the value in cash of one share of Arch Coal, Inc. common stock.  The shares of phantom stock are held by the Executive Officer through the Arch Coal, Inc. Deferred Compensation Plan (the &quot;Plan&quot;).  The shares of phantom stock acquired by the executive officer represent dividends attributable to amounts that the executive officer elected to defer under the Plan into a hypothetical investment in shares of Arch Coal, Inc. common stock.</footnote>
        <footnote id="F2">Shares of phantom stock are payable in cash on the date or dates elected by the executive officer, subject to the terms of the Plan.  The executive officer may transfer any and all of the phantom stock account into an alternative investment account at any time.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gregory A. Billhartz, Attorney-in-Fact</signatureName>
        <signatureDate>2006-12-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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