Abstract: A single crystal of Cu74.08Al23.13Be2.79 undergoes a martensitic phase transition at 246K and 232K under heating and cooling, respectively. Surprisingly, the martensite phase is elastically much harder than the austenite phase showing that interfaces between various crystallographic variants are strongly pinned and can not be moved by external stress while the phase boundary between the austenite and martensite regions in the sample remains mobile. This unusual behavior was revealed by Dynamical Mechanical Analysis and Resonant Ultrasound Spectroscopy. Transmission Electron Microscopy shows that the pinning is generated by dislocations, which are inherited from the austenite phase. Such dislocations can hinder the movement of stacking faults in the 18R martensite structure or twin boundaries between martensite variants.