A numerical implementation of the Raniecki Lexcellent (RL) (Raniecki et al 1992 Arc. Mech. 44 261–284, Raniecki and Lexcellent 1994 Eur. J. Mech. A 13 21–50, Raniecki and Lexcellent 1998 Eur. J. Mech. A 17 185–205) models for shape memory alloys (SMA) coupled with the heat equation is presented in this 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 and induced free vibration with a decreasing amplitude for isothermal and anisothermal conditions. The choice of material mechanical properties has been done in order to have phase transformations during the oscillations. The apparent damping and stiffness effects 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 fulfilled to be able to take into account the 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.