Considering the effects of shear distortion and rotator inertia, an improve Fourier series method is employed to analyze power flow of moderately thick rectangular plates with general elastic boundary support. The vibration displacements and the cross-sectional rotations of the mid-plane are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the discontinuity problems which encountered in the displacement and rotations partial differentials along the edges. So this method can be applied to general elastic boundary conditions. Then Hamilton’s principle based on Mindlin plate theory can give the matrix eigenvalue equation which is equivalent to governing differential equations of the plate. Finally numerical analyses are performed for the case where plates are excited by a harmonic point force, and the spatial distributions of vibration power flow are obtained.