The constitutive model for the mechanics of crystallizable shape memory polymers (CSMP) has been developed in the past [1, 2]. The model was developed using the theory of multiple natural configurations and has been successful in addressing a diverse class of problems. In this research work, the efficacy of the developed CSMP model is tested by applying it to the torsion of a cylinder, which is an inhomogeneous deformation. The crystallization of the cylinder is studied under two different conditions i.e. crystallization under constant shear and crystallization under constant moment.