The classical three-dimensional hydroelasticity of ships is extend to include the effect of fluid compressibility,which yields the three-dimensional sono-elasticity of ships.To enable the predictions of coupled transient or nonlinear vibrations and acoustic radiations of ship structures,a time domain three-dimensional sono-elastic analysis method of acoustic responses of a floating structure is presented.The frequency domain added mass and radiation damping coefficients of the ship are first calculated by a three-dimensional frequency domain analysis method,from which a retardation function is derived and converted into the generalized time domain radiation force through a convolution integral.On this basis the generalized time domain sono-elastic equations of motion of the ship hull in water are established for calculation of the steady-state or transient-state excitation induced coupled vibrations and acoustic radiations of the ship.The generalized hydrodynamic coefficients,structural vibrations and underwater acoustic radiations of an elastic spherical shell excited by a concentrated pulsating force are illustrated and compared with analytical solutions with good agreement.The numerical results of a rectangular floating body are also presented to discuss the numerical error resultant from truncation of the upper integration limit in the Fourier integral of the frequency domain added mass coefficients for the retardation function.