This paper discusses the development of a new procedure for finishing and hardening treatment by changing the kinematics of a deformation tool having a double-radius shape of the profile of the working surface, along with the determination of the stress-strain state in the site of elastic-plastic deformation and residual stresses in the hardened zone of the surface layer. The SOLIDWORKS 2018 software for 3D design and the ANSYS Work-bench 19.1 soft-ware using the finite element method were used to build a mathematical model of local loading. The temporary and residual stresses, the strain state in the loading zone, the depth of the plastic layer and the maximum value of the relative plastic deformation under various loading procedures of the working tool were determined. It was established that, at the reversible rotation of a double-radius roller, the values of temporary stresses are over 15% higher compared to those during static hardening, while the residual stresses are 5.7% higher. With the reversible rotation of the double-radius roll-er, the value of the maximum strain intensity becomes 2.11 times higher than that during static hardening. The intensity of the maximum residual stresses during the reverse rotation of the double-radius roller occurs at a depth 3 times greater than the indentation of the double-radius roller, rather than on the surface of the sample. The results of computer model-ling and numerical calculations indicate that the procedure of reversible rotation of a toroidal double-radius roller has the greatest influence on the intensity of the stress state in the deformation site, while the procedure of static hardening by a single-radius roller has the least impact. The obtained results suggest that the proposed technological process of surface plastic deformation based on the reversible rotation of the working tool will allow the radial tension to be reduced while maintaining the high quality of the surface layer of machine parts.