The process of thermoelastic phase transformations in shape memory alloys (SMA) can be caused not only by temperature changes, but also by isothermal loading (direct transformation) or by unloading (reverse transformation). Usually this effect is described by expressing the phase composition parameter – the martensite volume fraction through the characteristic temperatures of the beginning and the completion of phase transitions, which, in turn, depend on the acting stress. These latter dependences can be obtained as sufficient conditions for the fulfillment of the dissipative inequality and are in good agreement with the experimental data. According to the experimental data, the temperature of the onset of the inverse thermoelastic martensitic transformation in the SMA depends not only on the acting stresses, but also on the accumulated phase-structural deformations, and this temperature increases if the convolution of stress deviators and phase-structural deformations is positive and decreases if this convolution is negative. According to experimental data and known thermodynamic models of SMA behavior, based on the hypothesis of the additivity of the Gibbs potential of these materials, the increment in the temperature of the onset of the inverse transformation, which depends on the phase-structural deformation of the shape change, is proportional to this convolution. However, following experimental data the temperature of the onset of the reverse transformation in titanium nickelide increases very substantially with the growth of phase-structural deformations even at zero stresses. This effect can not be obtained using the above-mentioned temperature dependence of the onset of the reverse transformation through the convolution of stress deviators and phase-structural deformations, since at zero stresses this convolution is equal to zero. The first part of the work is devoted to the analysis of relevant experimental data for SMA based on iron and titanium nickelide. The influence of the nature of the initial deformations and their values, different ways of their setting and type of the strain state on the character of the temperature change of the beginning of the reverse thermoelastic phase transformation in the absence of stresses is studied.