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Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
Originator-Key-Asymmetric:
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 OFRHGlj4NyTxxvWFInaXDtbPU8A4iS/HaaGL2LwgsfLVIsaFHUsBv9t1DrHogmRl
 0b7S5rO8UngeNzaP5RB5uA==

<SEC-DOCUMENT>0001209191-04-003272.txt : 20040116
<SEC-HEADER>0001209191-04-003272.hdr.sgml : 20040116
<ACCEPTANCE-DATETIME>20040116104815
ACCESSION NUMBER:		0001209191-04-003272
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20040114
FILED AS OF DATE:		20040116

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			LEER STEVEN F
		CENTRAL INDEX KEY:			0001046086
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13105
		FILM NUMBER:		04528785

	BUSINESS ADDRESS:	
		STREET 1:		CITYPLACE ONE STE 300
		CITY:			ST LOUIS
		STATE:			MO
		ZIP:			63141
		BUSINESS PHONE:		3149942700

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
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2004-01-14</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001037676</issuerCik><issuerName>ARCH COAL INC</issuerName>        <issuerTradingSymbol>ACI</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001046086</rptOwnerCik><rptOwnerName>LEER STEVEN F</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>ONECITYPLACE DRIVE</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>ST. LOUIS</rptOwnerCity><rptOwnerState>MO</rptOwnerState><rptOwnerZipCode>63141</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>President &amp; CEO</officerTitle></reportingOwnerRelationship></reportingOwner><derivativeTable>
<derivativeTransaction><securityTitle><value>Phantom Stock</value></securityTitle><conversionOrExercisePrice><footnoteId id="F1" /></conversionOrExercisePrice><transactionDate><value>2004-01-14</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>107051.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F1" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><value>2009-01-02</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>107051.0000</value></underlyingSec
urityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>107051.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Restricted Stock Unit</value></securityTitle><conversionOrExercisePrice><footnoteId id="F1" /></conversionOrExercisePrice><transactionDate><value>2004-01-14</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>7115.0000</value></transactionShares><transactionPricePerShare><footnoteId id="F1" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcqui
redDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F3" /></exerciseDate><expirationDate><footnoteId id="F4" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>7115.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>7115.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">1-for-1</footnote><footnote id="F2">One third of the phantom stock units granted will vest immediately if the average trading price for Arch Coal, Inc. ("ACI")common stock is $30.00 or greater over a period of 20 consecutive trading days.  The remaining shares will vest immediately if the average trading price for ACI common stock is $40 or greater over a period of
 20 consecutive trading days.</footnote><footnote id="F3">Restricted Stock Units vest ratably over a three-year period.</footnote><footnote id="F4">There is no expiration date for the Restricted Stock Units.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Janet L. Horgan, Attorney-in-Fact</signatureName><signatureDate>2004-01-15</signatureDate></ownerSignature></ownershipDocument>

</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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