The Ti–Ni–Nb shape memory alloys are attracting recent attention for the wide transformation temperature hysteresis, which is caused by the As increase due to pre-deformation, since it is suitable for pipe couplings. To find out the origin for the As increase by pre-deformation, similar investigation was made by tensile tests, electrical resistance measurements, optical microscopy and transmission electron microscopy (TEM), for a Cu-13.8%Al-4.0%Ni (mass%) single crystal, and Ti-50%Ni and Ti-50.5%Ni (at%) polycrystals, which exhibit the thermoelastic martensitic transformation. The increase of As due to pre-deformation was confirmed in these alloys as well. When the single crystal was elongated to the end of the first stage of the stress-strain curve in the martensitic state, which corresponds to the rearrangement of martensite variants without permanent strain, As increased. On the other hand, the As increase in polycrystals was found to be closely related with the introduction of the permanent strain. Furthermore, the effect of pre-deformation was found to be erased by the subsequent reverse transformation, as is reported for Ti–Ni–Nb alloys. For that effect, we propose a mechanism, by focusing attention on the elastic strain energy stored during the thermoelastic martensitic transformation, which can explain the observed effect well.