Uniaxial tensile tests were carried out on T2 pure copper plate and H62 copper alloy subjected to identical heat treatment. The influences of different strain states on the damage degree of both materials were analyzed. It is found that the fracture and damage of T2 pure copper and H62 copper alloy were closely related to their microstructure under tensile loading. The shape factor of the studied materials showed a similar variation trend with increasing strain, while the shape factor of H62 copper alloy was larger than that of T2 pure copper and increased rapidly as compared to T2 pure copper. The relative shape factor of the studied materials showed very similar variation. H62 copper alloy entered the plastic deformation earlier than T2 pure copper, and hence its plastic deformation stage was shorter than that of T2 pure copper. Beyond a certain threshold, damage and deformation of H62 occurs faster than T2 pure copper. By virtue of exponential function, the normalized shape factor curves of the studied materials were fitted and the fitting equations were established, which revealed the relationship between the macroscopic deformation and microstructure of materials.