A numerical implementation of the RL model for shape memory alloys (SMA) is presented in the paper, adapted to high strain rate loading. The objective is to predict the time response of a 2D SMA structure subjected to an impulse force (duration 50 ms) and following free vibration with a decreasing amplitude. The choice of the material mechanical properties has been done in order to have phases transformations during the oscillations. The damping due to these phase changes is clearly identified when the results are compared with a linear model without induced martensite. The thermomechanical constitutive relation of the SMA has been fullfiled to be able to take into account time reaction when the strain rate is very high. The full model has been implemented in a finite element code and tested on a 2D sample.