This investigation is concerned with the determination of the sea state in terms of wave spectra. The phenomenon was calculated for two different bathymetries. The purpose is to develop a finite difference method with an upwind differencing scheme to g solve several formulations of the wave action conservation equation. The computations were done in the wave number space and the frequency direction space. For the case of a beach with constant slope the results were compared with the analytical solution. For the case of an elliptical submerged shoal, they were compared with experimental data. The results of the computer code showed a fairly good qualitative agreement with the actual values for a smooth distribution of input energy. / Master of Science