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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-05-14</periodOfReport>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001464287</rptOwnerCik>
            <rptOwnerName>ASSING FERNANDO RAFAEL</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>Sr. VP, Mrkt &amp; Bus. Dev.</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2010-05-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3666</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4881</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2010-05-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>156</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>12.01</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5037</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F6"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-05-14</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3666</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <value>2012-05-14</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3666</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7334</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On May 14, 2009, the Reporting Person received a grant of Restricted Stock Units (&quot;RSUs&quot;) under the Amended and Restated 2005 Tesco Corporation Incentive Plan (the &quot;Plan&quot;).  The RSUs vested on the anniversary date of a grant.  Under the terms of the Plan, the Company redeemed the vested RSUs for an equal number of shares of the Company's common stock.  The defined terms in this footnote are used in other footnotes throughout this Form 4.</footnote>
        <footnote id="F2">The Reporting Person received shares of the Company's common stock upon the vesting and redemption of an equal number of RSUs.  The Reporting Person received the shares at no cost.  The market value of the shares of common stock was calculated in accordance with the Plan at US$ 12.01.</footnote>
        <footnote id="F3">The shares were acquired by the Reporting Person pursuant to the Company's Amended and Restated Employee Stock Savings Plan (the Plan).  On May 14, 2010, the Company provided instructions to the Transfer Agent regarding the issuance of 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 2010 salary payments plus a benefit amount contributed by the Company as set forth in the Plan, funded the purchase of the shares.  The whole shares are held in the Reporting Person's name in the Plan and the Reporting Person has dispositive and voting control over the shares.  Any remaining amount from the contribution or benefit that was not sufficient to purchase a whole share remains on account with the Plan Administrator and will be added to the following month's amount.</footnote>
        <footnote id="F4">The share price was calculated in accordance with the Plan terms at US $12.01.  Based on the noon rate of exchange of the Bank of Canada on the date of calculation, the converted price is C$12.4231400.</footnote>
        <footnote id="F5">Includes shares of the Company's Common Stock held in Reporting Person's name in the Plan and purchased directly from the Company in accordance with the Plan.</footnote>
        <footnote id="F6">The Company redeemed RSUs from a grant received by the Reporting Person on May 14, 2009.  Under the terms of the Plan, there was no conversion price.</footnote>
        <footnote id="F7">The RSUs vest equally over three years on the anniversary of the grant date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>James A. Lank, Attorney-in-Fact</signatureName>
        <signatureDate>2010-05-18</signatureDate>
    </ownerSignature>
</ownershipDocument>
