The vibration characteristics of irregular elastic coupled plate systems are studied by Chebyshev-Ritz method in this paper, including dynamics and power flow control. Firstly, the accurate geometric model is established, and the coupling conditions and boundary conditions are simulated by artificial virtual springs. In order to facilitate integral operations, the irregular integral area is mapped into the regular integral area by a special coordinate transformation. Then all energy equations of the coupled system are established according to the first order shear deformation theory. The Chebyshev polynomial is used as the allowable displacement functions. Finally, the unknown coefficients in the allowable displacement functions are determined by the Rayleigh-Ritz technique. On the basis of the free vibration study, the dynamic behavior is studied by applying the external load to the system surface, including the forced response, the admittance and the power flow. While deriving the method, some modal verification experiments about coupled plate systems are designed. The innovation of the study is the establishment of the vibration analysis model of irregular elastic coupled plate systems based on the elastic theory, the coordinate transformation criterion and the two-dimensional Chebyshev-Ritz principle. The mechanism and control of energy transfers of the coupled plate system are studied by the power flow intensity analysis. The numerical results show that both the coupling condition and the boundary condition are important parameters in the vibration. This study provides some new insights into the vibration characteristics and energy transfer of the irregular elastic coupled plate system.