Jack-up designers, owners and operators are expanding their activities into seismically active areas such as Japan and Taiwan. Further development of expertise in seismic analysis of jack-ups is required to improve safety and reduce costs. At present, a linear elastic foundation model is used in seismic assessments. Improved understanding of foundation behaviour can lead to a significant reduction in conservatism. In this thesis a brief comparison of available foundation models is made. The radiation damping model has been improved, which is found to have minor effect on jack-up response. To capture non-linear foundation behaviour, a hypoplastic macro-element has been implemented in seismic simulation software OpenSees. This results in reduced non-linear resonance and an amplitude-dependent resonance-shift. The modelled loads at critical locations in the structure consistently decrease more than 25\% as a result. Plastic displacements and hardening are found to be significant for highly non-linear soils and severe earthquakes. This thesis demonstrates significant conservatism in the linear foundation model. Implementation of the proposed hypoplastic macro-element can thus reduce costs and increase demonstrated capabilities of jack-ups significantly.