During installation of a displacement pile, the soil around the pile is heavily distorted. The resulting changes in soil density and stress state around the pile determine the ultimate pile capacity. In most finite element models, the installation phase is not explicitly modelled. In this paper the full installation phase is modelled in two different ways, in a numerical code capable of large deformations. In the first approach the pile is fixed and the soil flows around the pile. This modelling approach requires somewhat unrealistic boundary conditions and requires that the results for the pile installation are for a non-stationary phase of the calculation, whereas formally only the values at the stationary full penetration phase are reliable. A second modelling approach has been introduced to overcome these limitations. In the new approach the initial conditions are set as a stress level, increasing linearly with depth, resulting from a gravity loading stage, and a stepwise penetration of the pile into the soil is prescribed. This approach updates the geometry of the problem domain and keeps updating the convective terms in a fixed mesh. Results are compared with experimental results from centrifuge tests. Although both models show the development of large effective vertical stress below the pile base and porosity change near the pile shaft, also differences with the experimental results are found. Especially the stiffness response during pile installation is difficult to model correctly.