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Martensitic transformation and phase stability of Ti50(Ni50−xCux) and Ni50(Ti50−xZrx) shape memory alloys are investigated based on density functional theory (DFT). According to the results of formation energy we calculated, upon substitution of Ni by Cu at levels of about 10.4 at.%, Ti50(Ni50−xCux) alloys lose the monoclinic martensite in favor of the orthorhombic martensite structure. The martensite monoclinic B19´ structure of Ni50(Ti50−xZrx) becomes more stable with increasing of the Zr content. The energy difference between austenite and martensite decreases when Cu < 10.4 at.%, and then increases slightly, which suggesting that Cu addition reduces the composition sensitivity of martensitic transformation temperature comparing with binary NiTi alloys. The energy difference decreases slightly firstly when Zr < 10.4 at.% and then increases sharply, which indicates that Zr addition increases martensitic transformation temperature dramatically. Furthermore, a geometric model is used to evaluate the thermal hysteresis. More interestingly, it is found that the lowest thermal hysteresis is achieved at 10.4 at.% for Cu-doped NiTi; whereas the thermal hysteresis increases with increasing of Zr. The electronic structures of austenite phase are also discussed in detail. [ABSTRACT FROM AUTHOR]