A numerical method for the computation of the dynamic behaviour of high-speed ships in waves is presented. The method is based on 2D+t theory, in which the three-dimensional (3D) flow around the vessel is replaced by several two-dimensional (2D) flows in earth-fixed transverse cross planes. The time development of the two-dimensional flows caused by the ship advancing through these transverse cross planes is computed. Together the two-dimensional flows give an approximation of the original three-dimensional flow. This approach simplifies the computations significantly and is appropriate for fast and slender ships since the flow will change only slowly along the ship. However, three-dimensional effects may still matter in some cases. The two-dimensional flows are treated as fully nonlinear potential flows. This means that viscous effects are neglected and that boundary conditions are kept in their nonlinear form and fulfilled on the instantaneous wetted hull and free surface. Therefore, most of the nonlinear effects can be taken into account. A boundary element method (BEM) is then used to calculate the flow numerically. A separation model is employed so that the non-viscous flow separation from round bilges can be computed. The developed method is used to compute the motions and forces on a semi-displacement vessel at high forward speed in calm water and also in incoming waves, which has not been achieved before using such a method. The results are compared to experimental data and generally very satisfactory agreement is found.