A new strategy of finite differences method is proposed for analysis of notched cross-section bars under elastic-plastic torsion. Relation curves of the elastic-plastic torque responding with different positions, angles and lengths of the notches in one section are obtained by numerical tests. It can be seen that these relation curves exhibit obvious nonlinearity. Meanwhile, the stress intensity factors can also be easily calculated by utilizing the results of above finite differences method. It provides an effective way for solving such elastic-plastic fracture mechanics problem.