SMAs are widely used for having two properties of shape memory and superelasticity. These alloys are usually available as wires and go under cyclic loadings in some practical applications, one of which could be indicated as the training process for creating two way shape memory effect (TWSME). Training in the form of applying cyclic loads until obtaining stabilized response and hence stability of non-elastic strains in SMA is one of the most effective achieving methods for getting TWSME. Using these alloys as dampers for controlling mechanical vibrations, due to their high damping capacities, is another case for imposing SMAs to cyclic loads. Hence the importances of studying and identifying SMAs behaviors under cyclic loadings are considered more than before. Thermo-mechanical coupling in shape memory alloys (SMAs) and its effect on high strain rates cause temperature variation of SMA during cyclic loadings. Temperature variation leads to dependence of cyclic responses of SMA in each cycle to previous ones. So, in analyzing cyclic responses in either transient or stable states, resolving all the previous cycles would be needed that it often leads to solving time consuming and complex equations. Although the loading condition in most of the studies on these alloys are assumed to be quasi-static, in the subject of investigating cyclic behaviors, consideration of models depending on the strain rate is inevitable. In this thesis, Firstly, a 1-D thermo-mechanical model is proposed and equations in continuum mechanics framework are extracted for stress-controlled and strain-controlled loadings. y developing a code in MATLAB, the boundary value problem is numerically solved and cyclic responses are extracted and compared with Kadkhodaei et al. results. Validation of equations and their results are showed by carrying out experimental tests on a nitinol wire in stress-controlled and strain-controlled cyclic loadings and proper agreement was observed between numerical results and experimental findings.The second part corresponds to the idea presented in order to cut the dependence of responses to temperature and predicting the number of loading cycles until getting stabilized response without solving all loading cycles. By assuming fixed temperature during cyclic loadings, the non quasi-static loading case may be behaved similar to the quasi-static state but SMA properties should be changed in such a way that prediction of the non-static responses at each instant of loading is possible. A pattern for variations in the mentioned properties and the number of loading cycles until getting stabilized response in different strain rates is proposed. The relations of the properties variations and the sensitivity of these relations coefficients to the loading situation are also investigated. The effects of transformation temperatures and wire diameter on variation of these parameters are also studied.Through the present approach in this research, non- static loading condition of SMA wires have the same behavior as the quasi-static state and the existing phase transformation relations could be used. However, in such a condition the effect of displacing lines and the effect of rotation of transformation strips in phase diagram are considered in order to predict SMA behaviors properly without solving complex thermo-mechanical equations. Key Words: Shape Memory Alloys (SMAs), Cyclic loading, Strain rate dependency, Thermo-mechanical coupling, Training.