Abstract: The mechanical behaviors of super-elastic shape memory alloy (SMA) are frequency-dependent. Based on Lagoudas’ multilinear one-dimensional model, some hypotheses are put forward by analyzing SMA’s testing data. That is, the slopes of the four phase transformation lines in the phase transformation diagram are frequency-dependent parameters, and the maximum residual strain is negative frequency-dependent. A frequency-dependent SMA constitutive model is presented. Some numerical simulations show that the simulated major loops agree well with the experimental results, but a little more differences can be seen between the simulated and experimental sub-loops. The proposed model at 0.003Hz and 0.08Hz is used to examine the dynamic responses of a SMA-spring-mass subjected to harmonic cyclic loading with different frequencies. Results show that SMA element can reduce the mass’ vibration response effectively, and that the difference between the controlled mass’ vibration response resulting from the diverse SMA’s models is valued to some extent.