The article presents the results of stress state analysis for workpieces from aluminium alloy 6063 cold-formed in a closed die. Mathematical methods of computer modelling (finite element method) and slip lines (slip-line field method) are used for the analysis. The experimental procedure for repeated cold deformation in a closed matrix (in several passes and/or cycles), the mechanisms of grain grinding and material hardening under the influence of grain-dislocation factors are described. The results of the stress state study of the material during cold deformation (at room temperature) show that the volume of the workpiece is mainly compressive stresses, the values of which are in the range from -273 MPa to -533 MPa. As found, due to the hydrostatic stress from the side of the punches and the side walls of the semi-dies, the workpiece is subjected to triaxial compression, which makes it possible to obtain volumetric spherical workpieces with ultrafine-grained nanostructure in a closed die with minimal processing cycles.