The microstructural model of the mechanical behavior of shape memory alloys was applied to describe the operation of a thermomechanical torsion actuator with a TiNi alloy working body and an elastic counterbody. The calculated dependences of а recovery strain, maximum stress in a cycle, and irreversible deformation on the cycle number were plotted for the working body of the actuator. It is shown that from cycle to cycle there is an accumulation of irreversible deformation, the rate of which gradually decreases. As a consequence, both the value of а recovery strainand the value of the stresses developed by the actuator decrease, which together leads to a decrease in the work output. The influence of the stiffness of the elastic counterbody on the specific work produced in the cycle was investigated. It is shown that the produced work depends non-monotonically on the stiffness of the counterbody and there is an optimal stiffness at which this work is maximized.