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In this paper, a kind of shape memory alloy (SMA) model based on multivariate statistical analysis was developed and applied in vibration control on rotor system with SMA bearing. Hysteretic nonlinear theory was introduced to interpret the difference between loading and unloading curve of SMA. Stepwise multiple regression method was applied in finding the relationship among strain, stress and temperature. The bifurcation characteristic of rotor system with shape memory alloy bearings (SMAB) was analyzed in improved centre manifold method. Finally the stability of rotor system with SMA bearing in PID control was proved. The new SMA model can describe the strain-stress curves of SMA in different temperatures well, and broadens the region of controlling temperature, which is helpful to vibration control.