Hamiltonian system for the problem on clamped Mindlin plate bending was established by introducing the dual variables for the generalized displacements in this letter. By separation of variables, the transverse eigen-problem was derived based on the sympletic geometry method. With the solved sympletic eigen-values, the generalized sympletic eigen-solution was derived through eigenfunction expansion. An example of plate with all edges clamped was given. The sympletic solution system was worked out directly from the Hamiltonian system. It breaks the limitation of traditional analytic methods which need to select basis functions in advance. The results indicate that the sympletic solution method could find its more extensive applications.