A power flow analysis of finite coupled Mindlin plates with a blocking mass at the junction of the coupled plates is investigated using the method of reverberation-ray matrix (MRRM). An exact solution is derived by the plate equations of motion to satisfy the boundary condition. The wave amplitude coefficients are obtained from the continuity conditions at driving force locations, and the line junction of two plates connected at an arbitrary angle. The blocking mass located at the junction of the two plates is modeled as a Timoshenko beam. The dynamic responses of the finite coupled Mindlin plates are verified by comparing with finite element method (FEM) results. The effects of the connected angles, blocking mass, and structural damping on the input power and transmitted power are calculated and analyzed. Numerical simulations of the finite coupled Mindlin plates with a blocking mass show that the present method can predict the dynamic behavior.