The software package DEFORM-3D is used to construct a mathematical model of the rolling of ribbed bars that makes it possible to determine the change in the shape of the bar, the stress state of the metal in the deformation zone, and the energy-force parameters of the rolling operation. The model accounts for the strain-hardening of the metal during cold deformation and the periodic nature of this process. Experiments confirm that the model adequately describes the actual deformation process. The results obtained from the model can be used to design new production equipment and tools for the given method of metal-shaping and to assess the feasibility of using existing rolling mills to form ribs on different types of flat-rolled semifinished products.