Abstract：Triangular meshes are always used in previous lower bound analysis by finite element method. For quadrilateral meshes，the equilibrium equations would be nonlinear on past form. To overcome this shortcoming，the weak form of equilibrium equations are established by integral over the whole elements and the equations are linear，so that，the linear programming can be used. On the other hand，there are less variables and constraint equations for quadrilateral element than triangle element，and so using quadrilateral element is more efficient than using triangle element. Examples show that the results based on quadrilateral elements are more accurate than that of triangle elements，which are consistent with general finite elements.