Based on the three-dimensional sono-elasticity theory for ship structures, the Green's function is incorporated and an integrated calculation method of acoustic radiation and propagation for floating bodies in shallow water considering the sound velocity profile is proposed. The near-field and arbitrary far-field acoustic radiation problem can be efficiently calculated. A numerical example of a rigid sphere is given and the results are compared with the finite element method solution to validate the reliability and demonstrate improvements in efficiency. The method is applied to an elastic capsular shell, verifying the applicability of the method for any elastic floating bodies.