In Part A of this chapter we consider torsion of circular shafts, for the cases of the linear elastic, linear viscoelastic, nonlinear viscous, and linear elastic, perfectly plastic material. Because of the simplicity of the circular geometry, the formulation of these problems is relatively straightforward. Then in Part B we consider the general noncircular shaft. We first formulate the linear viscoelastic problem from which the linear elastic problem is obtained as a special case, and then briefly consider the more complex nonlinear viscous problem. In all formulations the material is isotropic, and the loading is quasi-static so that inertia may be ignored.