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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-02-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000798287</issuerCik>
        <issuerName>PAM TRANSPORTATION SERVICES INC</issuerName>
        <issuerTradingSymbol>PTSI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000936926</rptOwnerCik>
            <rptOwnerName>WEAVER ROBERT W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>P.A.M. TRANSPORTATION SERVICES, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>297 W. HENRI DETONTI BOULEVARD</rptOwnerStreet2>
            <rptOwnerCity>TONTITOWN</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72770</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>23.22</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-02-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>16000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2007-03-15</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-08-27</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>16000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>72000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On August 28, 2002, the reporting person was granted an option to purchase 120,000 shares of common stock of the issuer.  The option vests in installments, beginning with 24,000 shares on the date of grant, and the balance in annual installments of 16,000 shares each on each March 15 through March 15, 2008, subject for each annual installment to the issuer's satisfaction of certain performance criteria for the immediately preceding year. The issuer has determined that the performance criteria for vesting of the March 15, 2007 installment has been met, resulting in that installment being deemed acquired.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Jerome M. Schwartz
Attorney-in-fact</signatureName>
        <signatureDate>2007-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
