There is a steadily increasing demand for the use of jack-up units in deeper water and harsher environments. To be confident of their use in these environments there is a need for jack-up analysis techniques to reflect accurately the physical processes occurring. The common modelling of spudcan footings as pinned or as linear springs is an over-simplification of foundation behaviour, and can therefore lead to overconservative design. This paper details the implementation of a work hardening plasticity model for spudcan footings on dense sand (named Model C) into a dynamic structural analysis program (named JAKUP). The motivation for this is to have a balanced approach to the analysis of jack-up units, with the non-linearities in the structural, foundation and wave loading models all taken into account. Wave loading is considered using NewWave theory, and the importance of random wave histories shown by constraining the deterministic NewWave into a completely random surface elevation. Examples are shown to emphasize the differences in predicted extreme response according to the various footing assumptions: pinned, linear springs and Model C. The role of plasticity theory for modelling foundations will be highlighted. Further uses of JAKUP in the understanding of the extreme response statistics and reliability of jack-up platforms are discussed. This paper is directed to those interested in the long-term reliability analysis of jack-up units.