Abstract: Both in light and heavy fluids, the impact of geometrical parameter of the elastic plate on its acoustic radiational damping was discussed. The solution to the coupled vibro-acoustic problem was presented. Based on energy theory, the acoustic radiational damping of the elastic plate was defined and the numerical formula of the plate＇s damping was educed. With the FEM and BEM, the acoustic radiation damping of the elastic plate was calculated numerically and the conclusion was made. The acoustic radiational damping of the plate in water is larger than that in air; the thickness of the plate shows little impact on its acoustic radiational damping; the acoustic radiation damping increases with the plate＇s size getting larger; and it is proved that the acoustic radiation damping of the plate will not change with the location of excitation.