This paper deals with a ®nite element method to compute the vibrations of a coupled ¯uid±solid system subject to an external harmonic excitation. The system consists of an acoustic ¯uid and a plate, with a thin layer of a noise damping viscoelastic material separating both media. The ¯uid is described by displacement variables whereas the plate is modeled by Reissner±Mindlin equations. Face elements are used for the ¯uid and MITC3 elements for the bending of the plate. The effect of the damping material is taken into account by adequately relaxing the kinematic constraint on the ¯uid±solid interface. The nonlinear eigenvalue problem arising from the free vibrations of the damped coupled system is also considered. The dispersion equation is deduced for the simpler case of a ¯uid in a hexahedral rigid cavity with an absorbing wall. This allows computing analytically its eigenvalues and eigenmodes and comparing them with the ®nite element solution. The numerical results show that the coupled ®nite element method neither produces spurious modes nor locks when the thickness of the plate becomes small. Finally the computed resonance frequencies are compared with those of the undamped problem and with the complex eigenvalues of the above nonlinear spectral problem.