To make economic use of offshore wind energy possible, foundation structures with minimum costs, but sufficient stiffness have to be designed. One foundation concept which has recently often been realized in this field is the monopile concept. Here the foundation consists of one steel pile with a large diameter of up to or even more than 5 m. This paper aims to investigate the behaviour of such a monopile under monotonic and cyclic loading taking the interaction between the pile and the subsoil into account. A three-dimensional numerical model using the finite element method was established. In this model the non-linear material behaviour of the subsoil is described using an elasto-plastic constitutive model. A special numerical scheme was developed to account for the effect of cyclic loading. With that, based on results of cyclic triaxial tests, the increase of pile displacements with the number of loading cycles can be quantified.