Shape memory alloys (SMAs) are good candidates for being used as passive dampers, strain sensors, stiffness or shape drivers. In order to develop the use of these alloys in structural vibration control, we present in this paper an implementation of a phenomenological model based on the Rl model (Raniecki et al 1992 Arch. Meh. 44 261–84) in a finite element code called COMSOL© which allows one to build automatically many loading cases in force or displacement. This implementation is used to simulate internal loops in order to characterize the stiffness and the damping effect by an equivalent complex Young's modulus approach under static strain offsets. The results clearly show the influence of the initial static strain offset and the amplitude of vibration on the damping and stiffness properties.