[Truncated abstract] Three-legged mobile jack-up rigs supported on spudcan foundations are used to perform most offshore drilling in shallow to moderate water depths, and are now capable of operating in water depths up to 130 m. With the gradual move towards heavier rigs in deeper water, and continuing high accident rates during preloading of the spudcan foundations, appraisal of the performance and safety of jack-up rigs has become increasingly important. A crucial aspect of this is to improve understanding of the mechanisms of soil flow around spudcan foundations undergoing continuous large penetration, and to provide accurate estimates of spudcan penetration resistance, avoiding excessive conservatism. Spudcan foundations undergo progressive penetration during preloading, contrasting with onshore practice where a footing is placed at the base of a pre-excavated hole or trench. However, spudcan penetration is generally assessed within the framework used for onshore foundations, considering the bearing resistance of spudcans pre-placed at different depths within the soil profile. The lack of accurate design approaches that take proper account of the nature of spudcan continuous penetration, which is particularly important in layered soil profiles, is an important factor in the high rate of accidents. ... It was found that when a spudcan penetrated into single layer clay, there were three distinct penetration mechanisms: during initial penetration, soil flow extended upwards to the surface leading to surface heave and formation of a cavity above the spudcan; with further penetration, soil began to flow back gradually onto the top of the spudcan; during deep penetration, soil back-flow continued to occur while the initial cavity remained unchanged. For spudcan penetration in stiff-over-soft clay, four interesting aspects of the soil flow mechanisms were identified: (a) vertically downward motion of the soil and consequent deformation of the layer interface; (b) trapping of the stronger material beneath the spudcan, with this material being carried down into the underlying soft layer; (c) delayed back-flow of soil around the spudcan into the cavity formed above the spudcan; (d) eventual localised flow around the embedded spudcan, surrounded by strong soil. At some stage during continuous spudcan penetration, the soil starts to flow back into the cavity above the spudcan. The resulting back-flow provides a seal above the penetrating spudcan and limits the cavity depth. It was shown that the current offshore design guidelines are based on the wrong criterion for when back-flow occurs. New design charts with robust expressions were developed to estimate the point of back-flow and hence the cavity depth above the installed spudcan. Load-penetration responses were presented in terms of normalised soil properties and geometry factors for both single layer and two-layer clay profiles, taking full account of the observed flow mechanisms. Further, guidelines were suggested to evaluate the likelihood and severity of spudcan punch-through failure in layered clays. Finally, the effect of strain-rate and strain-softening was examined, in an attempt to model real soil behaviour more closely. Adjustment factors were proposed to modify the design approaches developed on the basis of ideal elastic-perfectly plastic soil behaviour.