Based on the analogies between plane elasticity and thin plate bending problem, the thin plate bending under symplectic geometry form was solved by direct method. For thin plate with different boundaries, first the order of the governing equations was decreased to form a dual equation set, then the variable separation method was used, so the problem was transformed into an eigen-value problem. The following methods such as eigen-function, symplectic orthogonal relationship and symplectic expansion method were usded to obtain the analytical solutions of the thin plate. The numerical example shows that the method is effective and converges fast.