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Shape memory alloys (SMAs) have unique properties of pseudoelasticity and shape memory effect. Accordingly, they have been applied to commercial products and studied about for other new applications. However, their mechanical properties are nonlinear including hysteresis and vary depending on temperature, loading frequency and so on. To understand such complicated thermo-mechanical behaviours and to design structural systems including SMA elements optimally, a simple yet reasonably accurate constitutive model is necessary. In our laboratory, several types of constitutive models with an energy-based transformation criterion have been proposed. The features of the models are that they can consider (1) more than three phases/variants and (2) rate-dependent effect, and (3) can capture the deformation behavior quantitatively. In this paper fundamentals of SMAs, the constitutive models and some applications of the models are presented.