We have developed a composite grid method for the solution of the radiation problem We divide the domain into two different grids; one is a moving grid system and the other is a fixed grid system. This numerical method is applied to calculation of the radiation forces generated by the submerged plate oscillating near a free surface. The experimental data are compared with the numerical ones obtained by the present method and a linear potential theory. As a result, we can confirm the accuracy of the present method. Finally, Lie have evaluated the effect of nonlinear and viscous damping on the hydrodynamic forces acting on the submerged plate.