This paper introduces a strain-hardening plasticity model that describes the behaviour of caisson foundations when subject to combined vertical, horizontal and moment loads in clay. Development and calibration of the model is based on centrifuge experimental results, theoretical knowledge (bearing capacity and upper bound plasticity theory) and numerical finite element studies. It is applicable to integrated wave-structure-soil analysis. This is demonstrated with example dynamic analyses of a proposed three legged jack-up in over 140 m water depth. Results presented show how the caisson model can be used to study (a) optimum caisson geometries, (b) penetration and relative movement of the foundations, including permanent deformation in extreme events, and (c) comparative behaviour between different footing types.