Abstract Long wave propagation above a bottom topography such as tsunami waves can be modeled mathematically by applying shallow water wave equations. The finite volume method was developed to determine the numerical solution of shallow water wave equations. The method uses Lax-Friedrichs scheme for the determination of numerical fluxes at cell interfaces. Furthermore, the model and method was applied to the simulation of long wave propagation on a sloping beach. The simulation results shows that the present model and method has a power of simulation of long wave propagation of the tsunami wave on the beach topography with a slope.