An improve Fourier series method is employed to analyze the free vibration of coupled plates with general elastic boundary support, in which the vibration displacements is 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 partial differentials along the edges. And boundary conditions and coupled conditions are physically realized with the uniform distribution of springs on each boundary edge. Different boundary conditions and coupled conditions can be directly obtained by changing the stiffness of springs. Then Hamilton’s principle can give the matrix eigenvalue equation which is equivalent to governing differential equations of the plate, and all the eigenvalues can be obtained by solving the matrix equation. Finally the numerical results and the comparisons with FEA are presented to validate the correct of the method.