The work is devoted to the study of the effect of non-uniform hardening of a representative volume of a shape memory alloy (SMA) on the results of modeling the phenomenon of direct martensitic transformation in a rod of circular cross section from SMA, which proceeds at a constant torque. The problem is considered in the framework of the model of non-linear of straining of SMA in phase and structure transitions. When solving the problem, the hypothesis of flat sections for full deformations is valid. The temperature distribution over the cross-section of the rod from SMA during its cooling is considered homogeneous. In the course of the work, a comparison was made between the results obtained for different models of accounting for the martensite fraction of the representative volume of the SMA participating in the structural transition. The process of development of martensitic elements when cooling the rod from SMA is not considered in this paper. The problem is considered in a single-coupled thermomechanical formulation. It is believed that the cooling process is slow enough. The isolation of the latent heat of the phase transition and the dissipative effects are compensated by heat exchange with the surrounding medium. The problem under consideration is reduced to a system of differential equations, differently formulated in different parts of the region under consideration, the moving boundaries between which are not known in advance and are in the process of solving the problem. Therefore, this system cannot be integrated by standard methods. Proceeding from the elastic solution of the problem of torsion of rods of circular cross section, the maximum stress level is noted on the outer surface of the rod. Accordingly, the phase transition starts from the outer layers. In the general case, in the process of cooling, three regions can be distinguished in the cross section of the SMA rod. Near the outer layers, the phase transition has already been completed. The material is in the martensite state and deforms either elastically or by the mechanism of structural transformation. Near the axis of rotation, the phase transition has not yet begun. The material of the rod is in the austenitic phase state and deforms elastically. In the intermediate zone of the rod, a phase occurs, and under certain conditions, structural transitions occur. A dimensionless temperature parameter is used as the process parameter. In the course of the solution of the problem, the dependences of the dimensionless twist from the dimensionless temperature parameter, as well as the stresses over the cross-section of the rod for different cooling stages are obtained.