The tension leg platform (TLP) is a moored floating offshore structure whose buoyancy is more than its weight. The mooring system, known as tethers, is vulnerable to failure due to extreme (maximum and minimum) tensions. In the present study the reliability of these tethers under maximum and minimum tension (ultimate limit state) has been studied. Von-Mises failure criteria has been adopted to define the failure of a tether against maximum tension. The minimum tension failure criteria has been assumed to meet when the tethers slack due to loss of tension. First Order Reliability method (FORM) has been adopted for reliability assessment. The reliability, in terms of reliability index, and probability of failure has been obtained for twelve sea states. The probabilities of failure so obtained for different sea states have been adopted for the calculation of annual and life time probabilities of failure.