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In this research free surface motion governed by the shallow water equations is considered. A numerical scheme based on the finite element method, which is incorporated in the open source FreeFEM is used to simulate several wave phenomena. By carefully set the corresponding initial condition as well as boundary conditions, several numerical computations were conducted. Numerical simulations presented here are standing wave in a closed basin, wave shoaling over a decreasing depth as well as wave refraction. In all cases above, the existing analytical formula were used to validate the numerical results.