Shape Memory Alloys (SMAs) are widely studied as new materials with potential for use in various passive or active vibration isolation systems. Up to now, few papers deal with a precise description of their proper dynamic behaviour. However, it is important to clearly understand the dissipation mechanisms in order to optimize the design of a structure. We present here a detailed characterization of a Cu-Al-Be beam. The stress induced phase transformation austenite → martensite produces a strongly nonlinear behaviour. The aim of this study is to confront experimental results to a rheological model of the beam. The experimental setup consists in a cantilever beam excited by a light electromagnetic actuator. The response is measured by an accelerometer fixed at the free end of the beam. Stepped sine measurements have been performed around the frequency of the first mode of the beam under different excitation levels. The obtained frequency response functions strongly depend on the global vibration amplitude. Then a specific finite element model has been designed, taking into account the geographic repartition of the two phases inside the beam. The simulations show a similar behaviour and allow the interpretation of the experimental observations.