Compliant offshore TLPs are essentially meant for deep oil/gas exploration and are usually constructed on the seashore and then towed down to the particular location for anchorage. They are connected to the sea bed by means of pretension cables. The increased use of TLPs in deep waters and necessity of reduction of usually high value of pretension make the effect of variable tension in the tether dynamics more significant. This work presents the dynamic analysis of tethers and TLPs considering the linearly varying tension along the tether length. The modal analysis considers a linear cable equation for tether modeling subjected to tension which varies along its length. A Mathieu stability analysis is then performed for TLPs of different shapes and different water depth vis-à-vis of 527.8, 872, and 1200 m respectively to obtain the amplitudes of tether vibrations. The unstable modes of vibration are also verified. The resultant modal forms for the tether's dynamic model are then obtained in form of Bessel's function. From the numerical studies conducted it is seen that increased tether tension not only leads to a stable platform but also improves the stability due to increased hydrodynamic loading contributing to added mass. From the studies conducted it is also seen that the triangular configuration TLPs with increased initial pretension are more stable compared to four leg TLP in the first mode of vibration.