Abstract: The torsion deformation of the shaft is commonly considered, due to the diversity of its loaded forms and the complexity of the boundary constraints. Its computation and the internal force analysis are often not easy, involve the section-cut method and the unbinding of constraints. In this paper, a series method is put forward to compute the torsion deformation of the shaft with two fixed ends with the help of the generalized function and the periodic extension method, without using the section-cut and the unbinding of constraints and with simple steps. It can be extended to wider applications. In order to show the effectiveness of the method, the general treatment of the material mechanics and the method of this paper are compared through an example.