A deep-water jack-up oil rig must be designed successfully for the worst expected environmental condition. A wave-induced dynamic response analysis is one of the most important problems to assess the structural safety of oil rigs from the view point of fatigue strength. In the previous papers, the authors presented an analytical method of natural vibration of oil rigs and experimental data by full-scale measurement. This paper deals with the coupled effect of the global vibration, simple formula of the lowest natural frequency and wave-induced dynamic response analysis. Main conclusions are as follows : (1) Coupled vibration of sway mode and torsional mode for the global vibration of jack-up oil rig is discussed. Natural frequency of oil rig is not affected very much in the case of the symmetrical structure such as a rig with 4 legs, but shows ±5 per cent higher value in the case of the cantilever type oil rig with 3 legs. (2) For a jack-up oil rig with 3 legs, simple formula for estimating the lowest natural frequency of sway mode and torsional mode are derived. Calculated natural frequencies by these formula is found to be in satisfactory agreement with those obtained from full-scale measurement or from FEM analysis. (3) By taking account of the results of authors' investigation, calculation technique of wave-induced dynamic response is shown. Moreover, some examples of dynamic response spectrums for newly designed three deep water oil rigs were calculated using ISSC wave power spectral density.