A model is proposed for the calculation of the irradiation induced changes of the martensitic transformation temperatures of shape memory alloys. It considers the transition temperatures being determined by a chemical and a non-chemical term in the Gibbs free energy that can be affected by the irradiation induced changes of the vacancy density and the chemical ordering of the crystal structures. Numerical simulations for TiNi SMAs have shown that upon irradiation the austenite finish temperature Af can be raised slightly at the beginning stage. After that, both Af and the martensite start temperature Ms will decrease strongly and reach some stable values after extensive irradiations. Both the dose rate and the temperature of irradiations will affect the changes of Ms and Af. According to the simulation, the increase of Af at the beginning of irradiations is resulted from the irradiation induced point defect production that increases mainly the non-chemical term in the Gibbs free energy change of the martensitic transformation. The irradiation induced chemical disordering reduces both the chemical and non-chemical terms in the Gibbs free energy change and leads to the strong decreases of Ms and Af.