In preceding reports, authors studied on the two and three dimensional sound radiation problem and sound scattering problem from a vibrating elastic shells. Introducing the analytical and numerical solutions, we clarified the property of these phenomena. At the low frequencies, the radiation pattern is always dipole and not affected by the hull shapes, vibration modes and exciting points. On the other hand, at the high frequencies, the vibration mode of the shell near the exciting point becomes so complicated that the accuracy of numerical analysis will become worse due to the limitation of the element discretization or CPU time. In this report, we show the methods of approximate analysis of the low and high frequency regions. At the low frequencies, namely, when the sound wavelength becomes very long as compared with the hull size, we show that the low frequency approximation gives a good agreement with the exact solutions at ka <0.1, where k is the wave number of the time harmonic exciting force and a is the typical radius of the hull. At the high frequencies, namely, when the sound wavelength becomes short as compared with the hull bending wavelength, we propose a high frequency approximation in which a hull can be assumed as a infinite flat plate covered one side with the water. Then we show that the high frequency approximation gives a good agreement with the exact solution at the region where the frequency is larger than the critical frequency.