Abstract: In order to compare the merits and demerits of the finite element methods in the Lagrange system and the Hamilton system for the problem of layered plates and to choose appropriate numerical methods, several finite element methods are applied for the layered plates. With the use of MATLAB, an example is calculated and analyzed. Numerical results show that the conventional FEM (finite element method) and the improved FEM in the Hamilton System and the rational FEM in the Lagrange system all have their advantages, while the accuracy of the conventional FEM in the Lagrange system is poor.