Jerky elasticity was observed by dynamical mechanical analyzer measurements in a single crystal of the shape memory alloy Cu74.08Al23.13Be2.79. Jerks appear as spikes in the dissipation of the elastic response function and relate to the formation of avalanches during the transformation between the austenite and the martensite phase. The statistics of the avalanches follows the predictions of avalanche criticality P(E) proportional to E-epsilon where P(E) is the probability of finding an avalanche with the energy E. This result reproduces, within experimental uncertainties, previous findings by acoustic emission techniques.