The analytic solution of the eigenfrequencies and models of a rectangular thin plate with completed clamped supported was derived by the symplectic geometry method. Firstly, the basic dynamic equations for the elastic thin plate were transferred into Hamilton canonical equations. And then the whole variables were separated. Finally, according to the eigenfunction expansion method in the symplectic geometry, the explicit solutions of the eigenfrequencies and models of the rectangular thin plate with completed clamped supported were obtained. Because only the basic dynamic elasticity equations of the thin plate were used, it does not need to select the deformation function arbitrarily. Therefore, the solution is reasonable and theoretical. Moreover, some numerical results were presented to demonstrate the correction of formulations.