A mathematical model is derived to address the vibrations and sound radiation into a dense fluid, of a coupled system consisting of two semi-complex plates (i.e., supporting added mass, stiffeners, and having arbitrary elastic boundary conditions) linked in four points through multistage suspensions elements. The supporting plate is subjected to point, line or surface harmonic excitation, while the radiating plate is excited through the suspensions. Both plates are assumed to be baffled, and the radiating plate is fluid loaded. The model is based on a variational approach for the plates, and a matrix transfer approach is used to handle the coupling between the two-plates. The solution is found using a Rayleigh-Ritz expansion in terms of polynomial trial functions which are shown to allow for the arbitrary elastic boundary conditions and to facilitate the calculation of the radiation impedance matrix. The vibrations and noise design of the system is discussed. The main design indicators are the force transmissibilities between the different excitation and attachment points, the mean square velocity, the radiated power and the radiation efficiency of the radiating plate. Numerical examples are presented to show the effects of fluid loading and different design parameters (plates thickness, boundary conditions, added mass, stiffeners, etc.) on the radiated sound.