In this paper the problem of the direct phase transition under the constant torque for rods with solid circular cross-section from shape memory alloy (SMA) in the framework of non-linear model of straining of SMA in phase and structure transition is solved. The analysis is performed both in uncoupled formulation considering of elastic deformation and coupled formulation. Diagrams of dimensionless stress for the various stages of cooling rod are shown. Graphic dependence of the dimensionless parameter of twist from the martensite volume fraction and dimensionless parameter of temperature for different values of the dimensionless torque are obtained