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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-05-26</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001389533</rptOwnerCik>
            <rptOwnerName>Beierbach Barry E</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>
            <isOfficer>1</isOfficer>
            <officerTitle>VP (Mfg. &amp; Surface Prod. Eng.)</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-05-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>184.9061</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>9.65</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3442.2274</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The shares were acquired by the Reporting Person pursuant to the Company's Amended and Restated Employee Stock Savings Plan (the Plan).  On May 26, 2009, the Company issued shares to the Plan Administrator.  The share purchase price was calculated in accordance with the Plan and funds withheld from the Reporting Person's April 2009 salary payments plus a benefit amount contributed by the Company as set forth in the Plan funded the purchase of the shares.  The shares are held in the Reporting Person's name in the Plan and the Reporting Person has dispositive and voting control over the shares.</footnote>
        <footnote id="F2">The share price was calculated in accordance with the Plan terms at C$ 11.32.  Based on the noon rate of exchange of the Bank of Canada on the date of calculation, the converted price is US $9.65.</footnote>
        <footnote id="F3">Shares of the Company's Common Stock held in Reporting Person's name in the Plan, all which were purchased directly from the Company in accordance with the Plan.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James A. Lank, Attorney-in-Fact</signatureName>
        <signatureDate>2009-05-27</signatureDate>
    </ownerSignature>
</ownershipDocument>
