In order to investigate the underwater noise radiated from ships, as the first step, the study on the radiated sound from a rectangular panel is carried out. The vibration of a panel is represented by using the monopole and the dipole, and the sound pressure fluctuation radiated from the panel is calculated. The calculated sound pressure have a good agreement with the measured results. The sound pressure radiated from a panel vibrating with free surface around it is smaller than that covered by the baffle plate. And the radiation efficiency also becomes small when the panel vibrates with free surface around it. Therefore, the measured radiation efficiency of a rectangular panel vibrating with the free surface around it cannot be applied for the shell plate of actual ship. The natural frequency of the rectangular panel in the water is estimated by Kito's method, and the radiation efficiency of underwater sound of a panel is calculated by applying Maidanik's method. These results correspond with the mean value of the results which are calculated by using the monopole for a panel vibrating in a single mode. Then, it is considered that the radiation efficiency estimated by these procedure can be applied for a actual ship.