There was fulfilled a study of the effect of stresses applied to a specimen during the direct and reverse transformations in titanium nickelide shape memory alloy on the enthalpy of these transformations. A series of experiments realizing the martensitic transformations on cooling and heating under a constant shear stress (in torsion mode), same for both the direct and the subsequent reverse transformations has been carried out. Simultaneously were made the measurements of the shear strain and the differential thermal analysis, the methodology of which allowed obtaining estimates of the amounts of heat release and absorption. It was found out that with an increase in the stress from 0 to 100 MPa the enthalpy of the reverse transformation decreases by a factor of 2.5. It was noted that if the direct transformation is carried out under a stress, and the subsequent reverse transformation is performed after the specimen is unloaded, the heat absorbed during the reverse transformation decreases with the same stress change from 0 to 100 MPa only 1.3 times. A theoretical explanation for this phenomenon has been proposed. For this various factors affecting heat absorption during the reverse transformation are considered, such as the energy of the boundaries separating the orientation variants of martensite, the work produced by the applied stress on the phase deformation and the elastic energy stored in the material due to incompatibility of the phase deformation of the martensite plates. Evaluation of the elastic energy is based on the representation of a shape memory alloy, as a composite consisting of differently oriented martensite plates, and on taking into account the equilibrium conditions of stresses and the compatibility of the total strain. Comparison of the elastic energy stored due to the formation of martensite in the absence of stress and under the action of a stress of 100 MPa shows that its value corresponds to the change in the heat released during the reverse transformation. It is noted that the contributions of other factors listed above that affect the enthalpy of reverse transformation is much smaller and, moreover, cannot explain its decrease with increasing stress, since these contributions are directed only towards its increase.