The desire to anticipate and predict quality of the manufactured products, its compliance with the technical requirements of the customer at the stage of technology design leads to the development of various methods for theoretical analysis of the processes of plastic deformation. The purpose of these methods is to establish explicit patterns in the processes implemented using the intuitively clear mathematical functions. We have formulated a method for determining relative deformations at a local change in the shape of a closed shell of rotation through radial-rotational profiling. It is shown that it is possible, based on the derived analytical dependences, to predict dimensions of a semi-finished product at the design stage of the technological process. Up to now, there have not been any analytical expressions that would estimate an unambiguous dependence of deformation on the rollers radii ratio, on a billet, and on the magnitude of feed. It is established that the magnitude of relative deformations in three mutually perpendicular directions depends on the ratio of diametrical dimensions of deforming rollers and initial diameter of a billet. Comparison of calculation results, obtained in this work, with experimental data and existing expressions allows us to argue that a given method of calculation demonstrates the accuracy acceptable for the industrial production. This contributes to the possibility to control a field of stresses and deformations in order to manufacture an equally strong wheel rim at the stage of production preparation and a technological process design. The practical application of a given method of calculation would enable technologists and designers to take into consideration the deformation strengthening after each run of profiling. As well as to determine the operational dimensions of semi-finished products and to predict thickness of a finished product in radius transitions of the profile, that is, to intensify the considered process.