-----BEGIN PRIVACY-ENHANCED MESSAGE-----
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,
 HZjRfDKebxkviEM4Wh/hEspUM4/0oMYg9PTcUptYKZHOHJ5WoEvL6XmCeE9LEid3
 ZllbyAwtKaOx7jnncg1a4g==

<SEC-DOCUMENT>0001209191-03-033357.txt : 20031203
<SEC-HEADER>0001209191-03-033357.hdr.sgml : 20031203
<ACCEPTANCE-DATETIME>20031203141527
ACCESSION NUMBER:		0001209191-03-033357
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20031202
FILED AS OF DATE:		20031203

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			WOODRING KENNETH G
		CENTRAL INDEX KEY:			0001046096
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-13105
		FILM NUMBER:		031034939

	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>2003-12-02</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001037676</issuerCik><issuerName>ARCH COAL INC</issuerName>        <issuerTradingSymbol>ACI</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001046096</rptOwnerCik><rptOwnerName>WOODRING KENNETH G</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>ONE CITYPLACE 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>Exec. VP-Mining Operations</officerTitle></reportingOwnerRelationship></reportingOwner><non
DerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2003-12-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1775.0000</value></transactionShares><transactionPricePerShare><value>10.6875</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>
Common Stock</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2003-12-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1775.0000</value></transactionShares><transactionPricePerShare><value>27.5600</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value><footnoteId id="F1" /></securityTitle><trans
actionDate><value>2003-12-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>100.0000</value></transactionShares><transactionPricePerShare><value>10.6875</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>11107.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2003-12-03</value></transactionDate><d
eemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>100.0000</value></transactionShares><transactionPricePerShare><value>27.5700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>2358.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By 401(k)</value></natureOfOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Employee Stock Options</value></securityTitle><conversionOrExercisePrice><value
>10.6875</value></conversionOrExercisePrice><transactionDate><value>2003-12-02</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1775.0000</value></transactionShares><transactionPricePerShare><value>10.6875</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-02-25</value></exerciseDate><expirationDate><value>2009-02-25</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1775.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1975.0000</value></
sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeTransaction><securityTitle><value>Employee Stock Options</value></securityTitle><conversionOrExercisePrice><value>10.6875</value></conversionOrExercisePrice><transactionDate><value>2003-12-03</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>100.0000</value></transactionShares><transactionPricePerShare><value>10.6875</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2003-02-25</value></exerciseDate><expirationDate><value>2009
- -02-25</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>100.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1875.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Cashless exercise of employee stock options pursuant to pre-existing 10b5-1 plan.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Janet L. Horgan, Attorney-in-Fact</signatureName><signatureDate>2003-12-03</signatureDate></ownerSignature></ownershipDocument>

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</SEC-DOCUMENT>
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