The jack-up rig is composed by the platform for drilling operation and legs supporting it. About 400 of approximately total 700 mobile offshore drilling units (MODU) under operation in the world in 1984 are the jack-up rigs, namely the majority of MODU is the jack-up rigs because they have high maneuverbility for movement and operating performance under harsh environment. Since the structural strength is the main subject for the safety of operation, the various kinds of methods for structural analysis have been presented until now. But the development of methods for simplified practical structural analysis has been delayed due to less experiences in comparison with ships because it has been studied in only about thirty years after the first jack-up rig has been built. The author has developed and presented the simplified practical methods 1), 2), 3), 4) for strength and vibration analysis with high accuracy that is assured by the precise calculations using detail models and experiments for full scaled or 1/45 scaled, models. In this paper, the effects of water depth, jack spring, sea bed spring, wind incident angle, wave height and period to the structural characteristics of jack-up rig are studied by the results of parametric calculations with methods mentioned above for strength and vibration analysis and some design points are discussed.