The ductility of Cu – Al – Mn shape memory alloys at room temperature depends on the aluminium content. High aluminium contents make Cu – Al – Mn very brittle and unsuitable for plastic shaping. Two Cu – Al – Mn shape memory alloys were investigated. The ductile alloy CuAl7.8Mn9.5 (all contents in wt. %) could be easily cold rolled by 86 %. The alloy CuAl12Mn4.3 could be cold rolled by only 12 - 14 %. The amplitude dependence of damping of austenitic specimens increased with increasing degree of cold work, whereas the damping of martensiticaustenitic specimens decreased. These observations can be explained by the creation of stress induced martensite and therefore by new moveable interfaces like phase- and twin boundaries, which contribute to damping. Plastic deformation increases the dislocation density, too. Both the increase of dislocation density and the increase of martensite content can lead to a decrease of damping mainly for high deformation degrees. Same shape memory alloys have shown negligible hardness increase during cold rolling, too. This behaviour, untypical for metals, can be explained by the generation of new martensite and by the fact that the hardness of martensite is smaller than the hardness of austenite. Some aging effects of the specimen after cold rolling, which lead to decrease of damping, were detected. This can be explained by pinning of moveable interfaces by point defects and/or retransformation of martensite into austenite.