Abstract: The difference scheme of torsion problem of a barwith a sector cross-section under the polar coordinate system isderived. With Mathcad software, using theSuccessive over Relaxation Method, the difference values of the torsionstress function are determined; with the compound two-dimensionalSimpson integral formula, the torsion stiffness of the sectoralcross-section is obtained; consequently the difference solution to thetorsion stress is obtained. When the field angle is 2π, the thirdstress intensity factor at the crack tip is computed.