Mobile offshore jack-up drilling rigs are not custom-designed for a particular location but rated for typical operating characteristics, like water depths. They may be deployed at a number of different sites during their design life. Under the current guidelines, the jack-up is required to be assessed for its suitability for each new proposed location, assuming environmental loading conditions due to wind, waves and current corresponding to a 50-year return period storm applicable to the site. Traditionally, these assessments have been performed in two dimensions, simplifying the jack-up to a plane frame and the loading conditions to be in-plane with the rig's 'axis of symmetry'. This thesis introduces a computer program, named SOS_3D, for the fluid-structure-soil interaction analysis of jack-up response in three dimensions. Extensive experimental series have been performed to provide evidence for the generalisation of the foundationsoil interaction model to general six degree-of-freedom loading conditions and its applicability to load paths and stress levels relevant to jack-up spudcans. These experiments included (1) 1g single footing tests, (2) centrifuge single footing tests and (3) centrifuge model jack-up tests. The latter tests highlighted differences in response and mode of failure depending on the loading direction of the jack-up and re-iterated the importance of three-dimensional modelling. The numerical program SOS_3D introduced early in this thesis was shown to represent a useful tool for the prediction of jack-up behaviour under general combined loading in three dimensions. It provided reasonably good, conservative predictions of the experimentally measured jack-up behaviour.