In this paper a new evaluation method of the effective elastic moduli for heterogeneous materials with microstructures is presented. The effective elastic constants can be obtained to make two matrices numerically equal. One is the standard global stiffness matrix and the other is the stiffness matrix multiplied by an effective modulus, Young's modulus, shear and bulk moduli , Lame's constants. The results of Finite Element analysis show good agreement with the analytical upper bound values by the Paul's method with an application of the principle of minimum potential energy.