In this paper; first, a comprehensive understanding of temperature and stress induced phase transformation is presented and a thorough interpretation of martensitic phase transformation is presented. A numerical study of Brinson's model is then presented, in order to explain the capability of the model in reproducing the SMA characteristics under quasi-static thermomechanical loading. A MATLAB code was developed for the Numerical Simulation of Brinson's Constitutive Model. The stress strain curves obtained by the Brinson's model were used to simulate the behaviour of SMA wires and Beams under Quasi-static thermo-mechanical loading. Later in the end the applicability of Brinson's model for Hysteresis effects was studied by subjecting the beam model to two cycles of loading and unloading and then the Shape Memory Effect was studied. It was observed that the Brinson's Model needs some modifications for expressing Hysteresis Effects. However for one cycle of loading and unloading, the model well predicted the Super Elasticity and Shape Memory Effects.