The reducing of machine time during surface hardening by smoothening is possible by increasing in the contact length between the hardening element and part surface. We study the case: the indenter-working surface is a fragment of a cylindrical surface, which the symmetry axis is parallel to the axis of symmetry of the part hardened surface. We suggest that such a process scheme is corresponds to a 2D contact problem in which a cylindrical stamp moves in an inertial coordinate system along an elastic half-plane (circle). We tasking the boundary conditions in the contact zone, using the complex potentials developed in the works of L.N. Galin.