An effective theoretical method is proposed to study the vibration characteristics of rectangular plates with elastic boundary constraints，and the natural frequencies of rectangular plates are obtained experimentally. The elastic boundaries of a plate are modelled by a set of distributed springs. By employing the characteristic polynomial series as the admissible functions，the Rayleigh-Ritz method is applied to obtain the natural frequencies and modes of a rectangular plate with elastic boundary constraints. By changing the stiffness of the boundary springs，different boundary conditions of the plate can be realized，and the calculation efficiency is obviously improved. The structural natural frequencies calculated from the present theoretical method are in good agreement with the finite element and experimental results，which demonstrates the effectiveness of our theoretical model. In addition，the vibration characteristics of a rectangular plate under different boundary conditions，such as elastic-simply supported and elasticclamped boundaries，are studied experimentally. The influence of spring stiffness on the vibration behaviors of the rectangular plate is analyzed in detail.