Abstract: With the development of science and technology, one hasto develop new materials and to explorepotential of material properties. This paper presents thedevelopment of the elasticity theory with different Young's modulus in tension andcompression. There are fundamental problems for the finite element method (FEM) andengineering applications. In this paper, Ambartsumyan FEM computationalmodel, Jones' FEM computational model, Zhang's FEM computational model, andYe's FEM computational model are improved and discussed by an equivalentconcept. We find that the error of numerical results is apparent in the stiffness andstrength of the materials for engineering structures if uniform Young's modulus is used.