Finite element method (FEM) is used to solve physical problems involving complicated geometrics, loading and material properties which can not be solved by analytical method. This method is extensively used in the field of structural mechanics, fluid mechanics, heat transfer, mass transfer, electric and magnetic fields problems. In this method, a body or structure in which the analysis to be carried out is subdivided into smaller elements of finite dimensions called finite elements. In this paper, we consider higher order finite element (FE) for solving Saint-Venant torsion problem for a square cross-section. Explicit finite element formulas for global stiffness matrices for four sided quadrilateral elements have been also presented to compute the Prandtl stress function values and the torsional constants k of Saint-Venant torsion problem. In order to verify the accuracy, the obtained numerical results are compared with the exact solutions. The numerical solutions are in good agreement with the exact solutions. Numerical results show that the proposed method is quite efficient for solving this type of problem.