This study investigated the thermomechanical behaviour of the FCC↔HCP martensitic phase transformation in Co–32Ni single crystal during thermal cycling under constant tensile loading. It was found that under constant external stress both the forward FCC↔HCP transformation and the reverse HCP→FCC transformation yielded transformation-associated strains in the direction of the external stress. The magnitude of the strains generally increased with increasing magnitude of external stress. It was also evident that the external stress assisted both transformations, by increasing the critical temperature for the forward transformation on cooling and decreasing the critical temperature for the reverse transformation on heating. Consequently, the hysteresis between the two processes was reduced. The dependencies of the transformation temperatures on stress obey Clausius–Clapeyron law. Whereas the stress-induced forward FCC↔HCP transformation is consistent with other thermoelastic martensitic transformations in shape memory alloys, the stress-induced reverse transformation is in the contrary. The occurrence of the stress-induced reverse transformation is attributed to the multiplicity of crystallographic path of the reverse HCP→FCC transformation.