Coarse-grained commercially pure Cu was subjected to equal channel angular pressing at room temperature for 2 passes and 12 passes resulting in grain refinement down to the ultrafine scale. Uniaxial tensile testing revealed that as-ECAP Cu samples have very high strength, but low uniform elongation and elongation to failure, whereas small punch testing showed that strain in biaxial stretching of the as-ECAP Cu specimens was comparable to that in the coarse-grained Cu. Analysis of surface relief demonstrated extensive microlocalization of plastic flow into microshear bands during biaxial stretching of the as-ECAP Cu specimens. The effect of microstructure and stress state on formability of the material and the mechanisms governing its plastic deformation are discussed. It is suggested that although the high strength as-ECAP Cu exhibits poor ductility in uniaxial tension, in other strain paths such as biaxial stretching, it can show high formability which is sufficient for metal-forming processes.