Shape memory alloys (SMA) are good candidates especially for being used as passive dampers. In order to develop the use of these alloys in structural vibrations control, the dynamical behavior of a NiTi helical spring is led, and the damping effect investigated. First, compression tests on the spring are carried out. These tests allow us to notice the effect of the maximal compression displacement, the cyclic behavior and the compression rate on its mechanical behavior. A finite element model analysis of the compression tests is then proposed. In consequence, the materials parameters have been identified after a numerical convergence test. In order to characterize the dynamical behavior of the spring, the innovative tool called equivalent complex stiffness is developed and used. Finally, the one degree of freedom vibration equation is solved with this equivalent complex stiffness. The solution of this equation clearly shows the non linear dynamical behavior of the SMA spring and its damping potential.