A theoretical model is described for the behaviour of rigid foundations subjected to combined vertical, horizontal and moment loading. The model is based on a generalisation of the Winkler concept of subgrade reaction. Non-linearity of the stress-displacement response is introduced using the concepts of hyperplasticity, and the integration of the stresses over the foundation area is treated within this theoretical framework. The resulting model exhibits (with some limitations) behaviour that quite closely resembles that obtained from experiments and from more sophisticated numerical analyses. The performance of the model is illustrated by calculations for selected load and displacement histories. The primary purpose is to derive models, based on clearly articulated principles, that are capable of describing cyclic behaviour of foundations, and yet retain sufficient simplicity that they can be coupled with analyses of structures. Such models have important applications in the offshore industry for prediction of foundation response under environmental loads.