The effect of stacking fault energy (SFE) on the mechanical properties of pure Cu and alloys of Cu-2.2%Al and Cu-4.5%Al subjected to severe plastic deformation (SPD) was investigated. SPD was performed by equal channel angular pressing (ECAP) at room and cryogenic temperatures. It is established that the increase in the weight concentration of Al in the Cu matrix (a reduction of SFE) and decreasing the ECAP temperature leads to an increase of the strength characteristics. The observed tendency is caused by increasing of the role of deformation twinning.