In this paper, a general solution for torsion of hollow cylinders made of functionally graded materials (FGM) was investigated. The problem was formulated in terms of Prandtl’s stress and, in general, the shear stress and angle of twist were derived. Variations in the material properties such as Young’s modulus and Poisson’s ratio might be arbitrary functions of the radial coordinate. Various material models from the literature were also used and the corresponding shear stress and angle of twist were individually computed. Moreover, by employing ABAQUS simulations, finite element results were compared with the analytical ones.