TiNiCu shape memory alloy samples were irradiated by 1.7MeV electrons below the martensite finish temperature Mf. The transformation temperatures and the latent heat of phase transformation were measured by differential scanning calorimeter. The damage accumulation was determined by positron annihilation technology. The results indicated that the austenite transformation temperatures were raised, and the hysteresis was increased by the irradiation. The electron irradiation had a slight effect on Mf, and no detectable effect on the martensitic transformation start temperature Ms. The second lifetime of positrons were increased by the electron irradiation indicating the increase in the size and amount of vacancy clusters, which contributed to the observed change of the transformation characteristics.