Tethers of Tension Leg Platform (TLP) are a series structural system where fatigue is the principal mode of failure. The present study is devoted to the fatigue and fatigue fracture reliability study of these tethers. For this purpose, two limit state functions have been derived. These limit state functions are based on S-N curve and fracture mechanics approaches. A detailed methodology for the reliability analysis has then been presented. A sensitivity analysis has been carried out to study the influence of various random variables on tether reliability. The design point, important for probabilistic design, is located on the failure surface. Effect of wind, water depth, service life and number of welded joints are investigated. The effect of uncertainties in various random variables on tether fatigue reliability is highlighted.