The three-dimensional sono-elasticity method recently developed by Zou ((2014) Three-dimensional sono-elasticity of ships. PhD Dissertation, China Ship Scientific Research Center, China) and Wu ((1984) Hydroelasticity of floating bodies. PhD Dissertation, Brunel University, UK) is employed to explore the acoustic and vibrational characteristics of a propeller–shaft–hull coupled system. The acoustic field can be solved by introducing Green’s function for the ideal compressible fluid together with the Price–Wu generalized fluid–structure interface boundary conditions. The vibration of a ship structure is governed by the generalized equations, including added mass, damping and restoring coefficients. In order to discover the mechanisms underlying the acoustic and vibrational characteristics of the propeller–shaft–hull coupled system, numerical models for hull structures with a shaft and without a shaft are designated. Through modal analysis, the correlations of the line spectra of acoustic radiation and the corresponding vibration modes of the hull are clearly identified. Through further numerical analysis, the appropriate location of the base for the thrust bearing and installation schemes are recommended.