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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-11-21</periodOfReport>

    <issuer>
        <issuerCik>0001022705</issuerCik>
        <issuerName>TESCO CORP</issuerName>
        <issuerTradingSymbol>TESO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001364531</rptOwnerCik>
            <rptOwnerName>Quintana Julio M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3993 W. SAM HOUSTON PARKWAY N.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77043</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>16000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.0673</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>53790.1632</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The shares were purchased in eight separate blocks on the same day with the purchase price ranging from $5.02 - $5.10. The weighted average price for the 16,000 shares purchased was $5.0673. Upon request by the Commission staff, the Issuer, or a security holder of the Issuer, full information regarding the number of shares purchased will be provided.</footnote>
        <footnote id="F2">Includes 7,890.161531 shares held in Reporting Person's name in the Plan, 1,768.181531 of which were purchased directly from the Company in accordance with the Company's Amended and Restated Employee Stock Savings Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James A. Lank, Attorney-in-Fact</signatureName>
        <signatureDate>2008-11-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
