A mathematical model is developed for the coupling of two finite plates at an arbitrary angle for the prediction of the dynamic response and power flow at the coupling edge and at any cross section. The coupling at the joint edge considers bending, out-of-plane shear, and in-plane longitudinal (perpendicular to the joint edge) vibration. No constraint is imposed on the in-plane displacement perpendicular to the coupling edge. The exact solution for flexural mode shapes and resonance frequencies of rectangular plates with one edge free and the other edges simply supported is considered. This exact solution satisfies both the displacement and force boundary conditions, consequently it is used in the coupling of plate panels. An approximate relation is derived for prediction of the flexural resonance frequencies of higher-order modes with a reasonable accuracy. An approximate solution is presented for the in-plane response of the same plate panels when excited by in-plane forces perpendicular to the free edge. A simple expression is given for an approximate estimation of the cut-off frequencies for the different in-plane modes. The frequency response of the individual plate panels is presented as receptance functions for both flexural and in-plane vibration which are used in the plate coupling. The vibrational power injected into a plate by out-of-plane concentrated force and moment is computationally investigated. The importance of power input by a small moment excitation in some resonant bands even at low frequencies is highlighted. The spatial distribution of the components of flexural power transmitted by shear and moment across a section of the plate are investigated and the reason for the circulatory patterns of active power flow in plates is illustrated. The power flow characteristics in two plates coupled at an arbitrary angle is examined by a computational example. The effect of the coupling angle on the components of input power and power flow across the coupling edge is investigated. It is shown that the coupling of the two plates is mainly due to moment at frequencies up to the cut-off frequency of the first in-plane mode. Above this frequency, the coupling is due to out-of-plane shear and in-plane vibration with a diminishing participation of the moment in transmitting vibrational power through the coupling edge.