Abstract: Abstract Hamilton canonical equations have been derived by introducing the canonical functions in time direction,and a semi analytical method for the dynamic response of composite plates is provided.By separation of variable,conventional finite element discretization can be applied in the plane of lamina,and the exact solution in thick direction is deduced by the state space control method.Continuity of diplacements and stresses is ensured by applying the transfer matrix method,and the relational expression in the upper and lower surfaces is established,then the solution is obtained by means of the shot method.The results indicate that the number of variables is reduced greatly and the accuracy of the solution is enhanced.