In this thesis we investigate the net pressure load on an elastic body that is immersed in an inviscid fluid and undergoes compound vibration motion. The compound vibration motion consists of a rigid-body translational mode and a deformed vibrational mode. These two modes have the same frequency but different phase angles. Two simple kinds of elastic bodies, cylindrical and spherical shells, are considered in this thesis. Assuming the motion of the elastic body is not affected by the surrounding fluid, the pressure field in the fluid induced by the vibration of the elastic body can be determined by solving the acoustic equation subjected to suitable boundary conditions. After integrating the pressure on the deformed surface, we can obtain the net force exerted on the elastic body. Besides the phase angle in the time domain between the translational and deformed modes, we also consider the effect of the angle between the direction of the axis of symmetry of the deformed mode and that of the translational mode. The effects of various parameters, such as the vibration frequency, shape of the deformed mode, and phase angles, on the net force exerted on the elastic body are studied in detail.