Combined loading of shallow foundations is where a horizontal and/or moment load is applied to the foundation, in addition to the vertical load. This is one of the classic problems in geotechnical engineering. For offshore engineering applications the combined loading can be particularly severe due to wind and wave forces. As well, the cyclic nature of the loading means that assessing the structural dynamics is important, particularly if the structure is quite flexible, and this requires an accurate assessment of the foundation stiffness. Therefore to model properly both the static and dynamic behaviour of the structure requires linking the structural analysis with the foundation design, and ensuring that any changes in foundation stiffness are captured. A recent application where this is important is for offshore wind turbines, which feature as a prominent part of the renewable energy policy for many countries around Europe. Whilst a number of turbines are founded on mono-piles the option of using shallow foundations, either in the form of a gravity base or the more novel, but untested, suction caissons, is also pursued. Although the standard approach of using bearing capacity theory for shallow foundations is acceptable it is incompatible with doing dynamic analyses. A more recent approach for foundation modelling based on hardening plasticity captures the non-linearity of the foundation response and is therefore preferred. This paper outlines the offshore wind turbine application and then provides an overview of modelling of shallow foundations, focussing on hardening plasticity models.