Finding the analytic bending solutions of plates is of much importance in mechanical engineering.However,because of the difficulty in solving the complex boundary value problems of the governing high-order partial differential equations,benchmark analytic solutions are still rare.In this study,a Hamiltonian system-based governing equation is obtained for plate bending problems,then the equation is analytically solved for some fundamental subproblems with elaborate hypothetical boundary conditions,which only contain the undetermined coefficients.