One of the newest methods of severe plastic deformation (SPD) is Constrained studded pressing (CSP) method. A limitation of the constrained studded pressing process is the creation of surface cracks on the sheet. One of the most important factors affecting surface cracks is residual stress. In the present study, the effect of residual stresses on delaying the formation of microcracks on the surface and increasing the amount of applied strain on pure copper samples produced by CSP with the use of lubricant was investigated. Therefore, the strain distribution on the copper sheet for the first pass was studied using the finite element method (FEM). In addition, the evaluation of mechanical properties, microstructure, and residual stresses of the samples were studied before and after applying the CSP method. An optical microscope was used to examine the microstructure of the annealed and deformed copper sheets. The average grain size decreased from 35 μm for the annealed sample to 14 μm and 580 nm for the first and tenth passes, respectively. Changes in residual stresses also studied by X-ray diffraction. The residual stresses reached from +197.5 MPa for the annealed sample to -893.9 MPa in the 10th pass sample To check the mechanical properties, the microhardness Vickers test was used. The hardness of the annealed copper sample was 60.87 Vickers, which reached 85.85 VHN and 115 VHN after the first pass and tenth pass, respectively. Moreover, the hardness inhomogeneity factor (H.I.F) was used to calculate the uniformity of the Vickers microhardness distribution. Initially, the H.I.F increased and then decreased for the first pass, which means that the homogeneous distribution of microhardness increased.