In this paper,the analytical solutions for an elastic rectangular thin plate with opposite boundary completely clamped support and others free were derived by a Symplectic geometry method.Due to the fact that the basic elasticity equations of the thin plate were only used,it was not necessary to select the deformation function arbitrarily.Therefore,the solutions in this paper are much more general mathematically.In order to prove the validity of the formulations,numericam results were presented to be compared with those derived by other references.