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The deformation behaviour associated with the R-phase reorientation is investigated in a Ti-51.0 at%Ni polycrystalline shape memory alloy under the torsion-tension (compression) stress state, and special theoretical framework is developed to describe the observed alloy performance. The limit condition to start the reorientation process, represented as a surface on the axial stress-shear stress plane, is determined for the proportional loading path. The result is well described, not by the Huber-Mises condition (the J₂-theory) but by the model (the J₃-theory), by taking into account the third invariant of stress deviator through the concept of the shape function. The values of the shape function are determined experimentally. The basic experimental features of the deformation in the R-phase, such as the flow rule, the ratios of the reorientation strain rates and the dimensionlens ratio of the reorientation work, are compared with the predictions of theories that neglect the effects of pressure, compressibility of reorientation strains and effects of induced anisotropy. The J₃-theory turns out to be more realistic than the J₂-theory.