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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-02-01</periodOfReport>

    <issuer>
        <issuerCik>0000728535</issuerCik>
        <issuerName>HUNT J B TRANSPORT SERVICES INC</issuerName>
        <issuerTradingSymbol>JBHT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001190239</rptOwnerCik>
            <rptOwnerName>CHELETTE DAVID N</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>615 J.B. HUNT CORPORATE DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LOWELL</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72745</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <officerTitle></officerTitle>
            <otherText>VP, Treasurer</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2800</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.585</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11760</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2222</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.08</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13982</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2800</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.3</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11182</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2222</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.3</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8960</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock 401(k)</value>
            </securityTitle>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>I</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>104</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.1</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11063</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2012-07-15</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-08-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2012-07-15</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-08-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6900</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6900</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Right to Buy   Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.42</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>1999-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2009-11-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>800</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>800</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Right to Buy   Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.2</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2007-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-10-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Right to Buy   Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>20.365</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2012-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2015-10-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeTransaction>
            <securityTitle>
                <value>Right to Buy   Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>5.585</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2800</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.585</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2002-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2013-02-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2800</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Right to Buy   Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>7.08</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2008-02-01</value>
            </transactionDate>
            <deemedExecutionDate>
                <value>2008-02-01</value>
            </deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2222</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.08</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2004-06-01</value>
            </exerciseDate>
            <expirationDate>
                <value>2013-10-24</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2222</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11112</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes></footnotes>

    <ownerSignature>
        <signatureName>Debbie Willbanks</signatureName>
        <signatureDate>2008-02-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0202
4
2008-02-01
0000728535
HUNT J B TRANSPORT SERVICES INC
JBHT
0001190239
CHELETTE DAVID N
615 J.B. HUNT CORPORATE DRIVE
LOWELL
AR
72745
0
0
0
1
VP, Treasurer
Common Stock
2008-02-01
2008-02-01
4
M
0
2800
5.585
A
11760
D
Common Stock
2008-02-01
2008-02-01
4
M
0
2222
7.08
A
13982
D
Common Stock
2008-02-01
2008-02-01
4
S
0
2800
31.3
D
11182
D
Common Stock
2008-02-01
2008-02-01
4
S
0
2222
31.3
D
8960
D
Common Stock 401(k)
2008-02-01
2008-02-01
4
I
0
104
31.1
A
11063
D
Restricted Stock
0
2012-07-15
2016-08-15
Common Stock
3000
3000
D
Restricted Stock
0
2012-07-15
2015-08-15
Common Stock
6900
6900
D
Right to Buy   Stock Option
4.42
1999-06-01
2009-11-17
Common Stock
800
800
D
Right to Buy   Stock Option
12.2
2007-06-01
2014-10-23
Common Stock
12000
12000
D
Right to Buy   Stock Option
20.365
2012-06-01
2015-10-21
Common Stock
12000
12000
D
Right to Buy   Stock Option
5.585
2008-02-01
2008-02-01
4
M
0
2800
5.585
D
2002-06-01
2013-02-07
Common Stock
2800
16000
D
Right to Buy   Stock Option
7.08
2008-02-01
2008-02-01
4
M
0
2222
7.08
D
2004-06-01
2013-10-24
Common Stock
2222
11112
D
Debbie Willbanks
2008-02-04