The work is devoted to the simulation of the phenomenon of oriented transformation in the torsion of tubes and rods from shape memory alloy (SMA). An analytical and numerical solution of the problems is obtained. Modeling is performed in the framework of the non-linear model of straining of SMA in phase and structure transition in a single-coupled thermomechanical formulation. The flat sections hypothesis is accepted for total deformations. The cooling process is considered to be sufficiently slow, so that the temperature distribution over the thickness of the rod or tube is considered to be uniform. In the framework of the problem of oriented transformation for a thin-walled tube, various variants of the function of the model responsible for the contribution to the phase deformation of the processes of nucleation and development of martensitic elements are considered. As the parameter of the process of oriented transformation, the volume fraction of the martensite phase for thin-walled tubes is favored, and for rods of solid circular cross section and thick-walled tubes from SMA, the temperature is. The problem is reviewed in three stages. At the first, a direct martensitic transformation occurs under the action of a constant torque. At the second stage, there is an elastic unloading. It is noted that at the time of the start of unloading both the stress-strain and the phase state are inhomogeneous. After complete unloading, phase-structural and elastic deformations are observed, which do not obey the Saint-Venant’s hypothesis separately. As a result, the unloading process is simulated numerically. After unloading, based on the stress state of the SMA sample, it is determined whether the phase transition will continue immediately or additional cooling of the sample will be required. The third stage is the cooling of the sample to the complete termination of the direct martensitic transformation. In the work, dependences are determined of the dimensionless twist from the phase composition parameter and the dimensionless temperature parameter for different values of the dimensionless torque under the action of which the first stage of the oriented transformation proceeded. Dimensionless stresses distributions are plotted along the cross-section of the rod for various cooling stages.