Abstract: By considering the nonlinear term in Hellinger-Reissner variation principle, the buckling formulation in Hamilton system is derived. Its general solution is obtained according to the united theory on general solutions of systems of elasticity equations. As examples, a beam and a composite beam with two ends simply supported were studied. A plate and a composite plate with four edges simply supported were also investigated as instances. The results were compared with the classical ones. The results obtained are the exact solutions based on the exact elasticity theory (without any geometrical hypothesis). This paper provides a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation.