Abstract: Shape Memory Alloy (SMA) is one class of intelligent material system which has shown broad application area. Vibration control of structures using SMA material is one of important research direction which is well-shown applicable value of this advanced material. In this paper, a brief introduction of the main mechanical behavior of SMA including the shape memory effect and superelasticity is presented at first. The constitutive equations ultilized in describing the mechanical behavior of SMA are also review...