Abstract: Using the concept of base forces, the problem on the explicit tensor expression of element stiffness matrix for finite element method was identified, mathematic model of finite element method on potential energy principle was established by using an explicit expression. A code on the base forces finite element method was developed by using MATLAB computer language. The approach was used to solve several problems of elasticity theory, and various shape elements were compared and analyzed. The numerical results are consistent with those of the theoretical solutions. The availability of this approach is verified.