In mechanical design and application, in order to calculate torsion angle and shear stresses of prismatic bars with seetorial cross-section undergoing extemal couples, the numerical method is presented. The torsion equation is nonhomogeneous partial differential equation. First, using the method of separation of variables, torsion stress function is acquired in polar coordinate. Then, the method of boundary collocation is improved to calculate the undetermined parameters. Finally,approximate numerical solutions of stress function and shear stresses in cross-section are obtained. It is given the several calculation results of shear stresses of prismatic bars with different vertex angles. These results show that the method has some precision and application feasibility in engineering design. The method of separation of variables is combinied with the method of boundary collocation simplified calculation process.