Recent development of underwater acoustic devices causes a need to study the underwater sound radiated from the ship. Such underwater sound has two sources, the one is mechanical due to the vibration of main or auxiliary engines and the other is hydrodynamical due to the propeller cavitations and flow noise. In the present report, we deal with the former one, that is, the sound radiation problem in which the vibration of engines is transmitted to the ship hull and then its hull vibration is radiated into the water as sound. In order to study the fundamental characteristics, as an example, we solve a two dimensional circular cylindrical shell floating on the free surface which vibrates periodically and show the mutual interaction between the shell vibration and the acoustic field of the surrounding water especially its far field property.