A general modeling method is developed for the vibroacoustic analysis of an arbitrarily restrained rectangular plate backed by a cavity with general wall impedance. The present method provides a uniform way to obtain the solution of the coupled structure-cavity system, making changes of both boundary conditions of the plate and impedance of the cavity walls as simple as the modifications of geometrical or material parameters without requiring any altering of the whole solution procedure. With the displacement of the plate and acoustic pressure in the cavity expanded as double and triple Chebyshev polynomial series, respectively, a simple yet efficient solution to the problem of the modal and vibroacoustic behavior of the coupled system is obtained under the Rayleigh–Ritz frame. The current method can be applied to handle strong structural-acoustic coupling cases and this is illustrated explicitly by considering one case with a shallow cavity and very thin plate while the other with a water-filled cavity. The spatial matching of velocity at the interface is checked by numerical examples. The excellent orthogonal and complete properties of the Chebyshev series representations enable excellent accuracy and numerical stability. An experiment is conducted to validate the present method. In addition, the accuracy and reliability of the current method are also extensively validated by numerical examples and comparisons with theoretical solutions, finite element results, and results available in the literature. The effects of several key parameters are analyzed, including structural boundary conditions, plate thickness, cavity depth, and wall impedance.