Shape memory Alloys (SMA) are widely used as new materials with higher potential in implants, self expanding NiTi stents, etc. for medical applications and in actuators, micro actuators, components for isolation of vibrations, etc. for non-medical applications. In this study, shape memory effect, superelasticity, and excellent damping capability, three special characteristics of this material, are discussed and an extended one-dimensional constitutive model for prediction of superelastic behavior is proposed. The model is based on strain as control variable (strain driven). Stress induced austenit-martensite evolutionary equations are first proposed and time discrete model is then obtained through backward Euler scheme. The solution of the time-discrete model is approached by a modified return map algorithm for phase transition. Then, tangent modulus is used for the quadratic convergence of the Newton method ill the phase transition conditions. Muller model helps us to predict material behavior in the pseudo-elastic hysteresis. In the next step, extended solution algorithm is proposed and different experimental test results are discussed. Finally, the proposed model results are compared with the result of some experimental studies, which shows good agreements.