In this paper the double coupled problem of torsion of thin-walled tubes from shape memory alloy (SMA) is widely used in damping devices at the seismic influences, as well as working body torsional actuators in aerospace systems is solved. Consideration of the problem is carried out in the framework of non-linear model of straining of SMA in phase and structure transition. The numerical simulation, considering separation/absorption of latent heat of thermoelastic phase martensitic transformation and dissipative properties of SMA, as well as convective heat transfer to the environment, possible to obtain superelasticity curves (dimensionless stresses – total deformation), and graphic dependences of a dimensionless parameter of temperature from the volume fraction of the martensite phase for any values of the loading rate and heat transfer coefficient with the environment.