Abstract: This Paper Presnted a sort of high accurat mixed element's shape function in the beam analysis. The number of freedom at a node are expanded with shear force and the bending moment in the displacement method of the beam analysis. Using weighted residual method, the stiffness matrix and load vector of an elent are derived from the governing equation of the beam, so are the axial force and displacement. If the applied loading function is not more than cubic polynomials.The exact solution is obtained for the beam problem.with the unified handle, it may be used to the structural problems.It is a new practise that the weighted residual method is used to the frame systems.The method has successes on some examples.