Certain class of offshore structures exhibit highly intense nonlinear behavior called springing and ringing. Dynamic response of compliant structures like Tension Leg Platforms (TLP) under impact and non-impact waves responsible for ringing and springing phenomenon is of large interest to marine engineers. This paper develops a mathematical formulation of impact and non-impact waves and discusses the method of analysis of TLPs of triangular geometry under these wave effect; response of square and equivalent triangular TLPs are compared. Heave response in square TLPs show bursts but there are no rapid build-ups; gradual decays are seen in most cases looking like a beat phenomenon while such results are not predominantly noticed in case of equivalent triangular TLPs. Ringing, caused by impact waves in pitch degree-of-freedom and springing, caused by non-impact waves in heave degree-of-freedom in both the platform geometries are undesirable as they pose serious threat to the platform stability. Analytical studies conducted show that equivalent triangular TLPs positioned at different water depth are less sensitive to these undesirable responses thus making it as a safe alternative for deepwater oil explorations.