The NiTi alloys has the disadvantage of having a large hysteresis. Hysteresis could be generally described as an effort to return to a previous situation. For minimizing the hysteresis we replace a part of Ni atoms by Cu in the equiatomic NiTi alloy. Copper addition, as a ternary alloying element, results in increasing the characteristic temperatures of the martensitic transformation, when compared to a binary NiTi alloy. Moreover, copper causes good stability of characteristic temperatures and good corrosion resistance, narrow transformation hysteresis. In this project we are interested to study the effects of an addition a third element to the NiTi alloy in an attempt to reduce the effect of hysteresis in SMA actuators. The main aim of this project is creat a mathematical model to show that minimize the hysteresis can be done by adding the copper element to a NiTi to be a Ni(50−X)Ti50CuX alloy (where X = 10, 12, 14, 16, 18, and 20 at%) instead of Ni(50)Ti(50).