This work presents the texture evolution of the austenitic phase of a copper based shape memory alloy by neutron diffraction. The Cu-11%Al-0.62%Be (in mass %) alloy was subjected to cold and hot rolling processes. The texture of the rolled samples at reduction rates of 5%, 10% and 15% respectively were compared to those of the raw material. A <001> partial fiber is observed for the raw material and cold rolled samples whereas the texture of the hot rolled sample is mainly characterized by a <111> fiber. The influence of these mechanical treatments on the transition temperatures and the hysteresis evolution was also analysed by following the integrated intensity of the {220} reflection of the austenitic phase. A shift towards low temperatures of martensitic transition temperatures is observed with the increasing of the rolling rate.