Shape memory alloys (SMAs) are identified with two main characteristics; shape memory effect, and pseudoelasticity; temperature and stress induced phase transformations respectively. By pseudoelasticity, SMAs sustain large amount of strain, without permanent plastic deformation, and recover it upon heating. Constitutive models have been proposed for single/polycrystalline SMAs. The first practical model, was proposed by Tanaka (1985, 1986). That consisted of one equation for stress vs strain, temperature, and martensitic phase fraction (MPF), and a set of kinetic relations, for MPF during phase transformations. Liang and Rogers (1990) proposed a model utilizing a simpler kinetic relation. Brinson (1993) developed a more versatile and realistic model, by incorporating the temperature and stress induced MPF into the kinetic relations. That predicts the material behavior throughout the entire temperature range. This paper presents a comprehensive understanding of temperature and stress induced phase transformation. A thorough interpretation of MPF and critical stresses of phase transformation versus temperature are discussed and capabilities of Brinson's model in reproducing the SMA characteristics under quasi-static thermomechanical loading are demonstrated. Such in-depth elaboration of these relationships has not been reported in the literature; yet is it is essential for capturing the nature of superelasticity. Exploring the capabilities of Brinson's model facilitates applications of autoadaptive materials in structural or mechanical systems.