The main objective of this study is to get an insight into the dynamic behaviour of a jack-up platform with lattice legs, in elevated condition. The main parameters to be examined are: a. Water loads b. Deck motions c. Hydrodynamic damping These parameters will ba investigated for the excitation ot the platform by a regular wave as weIl as a stochastic sea state represented by a JONSWAP wave spectrum. An attempt will be made to tind statistical distribution functions tor the water loads and the platform motions for the case of aspectral reprentation of the waves at sea. A numerical approach to handle jack-up dynamics is developed, together with the necessary computer programs, applicable to a wide range of jack-up platforms and environmental conditions. Much attention will be paid to comparin; frequency domain analysis and time domain analysis. In order to get a verification of the general results, the resulting numerical model will be applied to a Russian platform, the Kolskaya, which is shown on the cover of this report.