A numerical model has been developed for the simulation long wave propagation and run-up accounting for the bottom friction. Shallow water continuity and momentum equations are solved numerically by a two time step finite difference method. The upwind/downwind method is applied to the nonlinear advection terms and the continuity equation. Effects of damping and bottom friction on the computations are investigated. Since the equations lose their validity when waves break, wave breaking has been checked at every step of the computations. A point can be either wet or dry at different time levels. A moving boundary description and staggered grid are used to overcome the difficulty of determining wet and dry points. Equations are solved by the finite difference approximations of second and third order accuracy. Furthermore, space filters are applied to prevent parasitic short wave oscillations.