As mobile jack-up drilling rigs continue to move into deeper waters and harsher environments there is an increased need to understand their behaviour under storm loading conditions. To improve the assessment of jack-ups for a specific site it has become necessary to analyse these units in three dimensions with models that appropriately reflect the physical processes occurring. This motivated the development of SOS_3D, a computer program that takes a balanced approach to all three interrelated components of the structure, the foundations and the environmental loading in three dimensions. Geometrical structural nonlinearities are incorporated using a path-dependent formulation of beam-column theory to specify an incremental stiffness matrix. A six-degree of freedom strain-hardening plasticity model simulates the complex interaction between the soil and the spudcan foundations. Advanced formulations for environmental loads are also implemented. In this paper, the results of three-dimensional jack-up analyses (i) are compared with two-dimensional simulations; (ii) highlight the importance of dynamic assessments; and (iii) describe the influence of wave spatial dispersion and loading direction on the response.