Self-installing mobile jack-ups platforms retain a dominate role in the exploration of offshore oil and gas in water depths up to around 120 m. However, significant challenges in assessing their stability and dynamic performance under large storm loading remain. For instance, their long slender truss-work legs and large inverted conical spudcan footings cause the natural period of the jack-up to approach the dominant frequency of ocean waves. The spudcan stiffness is also non-linear and requires a methodology to integrate it numerically within the environmental loading and structural analysis. Modern jack-ups are also increasing in size. Spacing of over 50 m between legs requires accurate evaluation of both the magnitude and timing of storm loads on each leg. To address these issues, this paper details a methodology for numerically integrating the fluid, structure and soil behaviour for large three-legged jackups. A six-degree-of-freedom strain-hardening plasticity model for integrating the load-displacement behaviour of spudcan footings into three-dimensional structural analysis is reviewed. It will be shown that non-linear behaviour of soils can be accommodated within an established theoretical framework, and as the response of the foundation is expressed in terminology consistent with structural mechanics, the models can be coupled directly to the numerical analysis of a structure. The influence of the spatial variability and directional wave spreading on jack-up response is also investigated. Example analyses of a jack-up installed in sand highlight the effect of wave direction, spreading function and foundation modeling assumption on the dynamic jack-up response.