Based on the Brinson constitutive model of SMA, a piecewise linear model for the hysteresis loop of pseudo-elasticity is proposed and applied in the analysis of responses of an SMA-spring-mass system under initial velocity activation. The histories of displacement and velocity of the mass, and the response of stress of SMA are calculated with Brinsons model and the piecewise linear model. The difference of results of the two models is not significant. The calculation with piecewise-linear model needs no iteration and is highly efficient.