A simple mathematical model is developed based on the single-degree-of-freedom analogy and principle of conservation of energy evaluating various modes of Vortex-Induced-Vibration (VIV) of a jack-up with cylindrical legs in regular waves. Similar to uniform current, mass ratio, damping ratio and mode factor are found to be the important parameters controlling the cross-flow VIV and radius of gyration also for the yaw VIV. Criteria for the initiation of the mentioned VIV modes are developed for the cases of a single 2D cylinder experiencing planar oscillatory flow, four rigidly coupled 2D cylinders in rectangular configuration experiencing planar oscillatory flow and jack-up experiencing regular waves. The newly developed VIV model is validated by a set of experiments conducted in a wind, wave and current flume. The importance of mass damping parameter is further demonstrated in suppressing VIV in regular waves. The mathematical method will equip engineers to consider the effect of VIV due to regular waves in jack-up designs.