Abstract: The vibration and sound radiation of a submerged spherical shell in the time-domain are studied by Laplace transform method, in which a pulse force is acted at the apex of the shell. The numerical results for the case of long pulse show that the different vibrating mode and the resonant or beat radiation sound are excited by the different filling-frequencies and little sound is radiated by some vibrating modes. For the case of short pulse the waveforms of the pulse become widened and deformed when the pulse propogates between apexes of the shell. Then, the Doubly Asymptotic Approximations (DAA2) and Kirchhoff's Retarded Potential Formulation (KRPF) are used to solve the same problem. It shows that the results of DAA2 and KRPF method have a good agreement with the results of Laplace transform method.