In this research, the residual stresses distribution resulting from one of the severe plastic deformation methods called Constrained Groove Pressing in pure copper sheets has been studied experimentally and numerically. For this purpose, after the initial preparation of each sample, the mentioned process is applied to the samples up to three passes. After each pass, the residual stresses in these samples in both directions of their length and width have been measured experimentally. To measure the residual stresses in these samples, the contour method, which is a relatively new, effective, and accurate method in providing a two-dimensional residual stress map, has been used. The results indicate that the residual stresses on the surfaces of the samples are compressive and by moving towards the central layers of them, these stresses are converted into tensile residual stresses. The distribution of residual stresses along the length and width of the samples is reported to be relatively uniform. In another part of this research, numerical simulation of the Constrained Groove Pressing process in ABAQUS finite element software is discussed. In this simulation, Johnson–Cook model is used as a constitutive model. The average error of residual stress distribution between the simulation and contour method was about 18% which shown a good agreement.