In this thesis results from numerical simulations of long wave run-up on composite beaches are presented along with the analytical solution to the linear problem. The purpose of this study is to find out which parts of the slope are crucial with respect to the angles. The numerical models used are based on non-dispersive shallow water theory in which an essential assumption is that the wavelength is large compared to the depth. The results suggest that the linear run-up height on a composite slope can to a great extent be estimated analytically by the parameters describing the slope segment closest to the shoreline. For nonlinear waves the results are divided into categories. For strictly non-breaking waves the run-up height is found to be similar to the linear run-up height. It was found to be higher if the incident waves had a steep wavefront. For breaking waves the run-up height was found to be much lower. This is due to the dissipation of energy during the breaking process. However, the results suggests that even for breaking waves the run-up height is determined by the slope parameters in the region where the depth approaches zero.