The paper presents the results of studies of the effect of nano-amplitude vibrations of steel samples in a constant and uniform strong magnetic field on some of their physical and mechanical characteristics. Various technological schemes are considered, in which broadband excitation of samples is applied using piezoelectric exciters that convert an electrical signal of constant amplitude in the range from 20 Hz to 20 kHz in the form of "white noise" into a resonant spectrum of natural mechanical vibrations of the samples. The results of such impacts on samples in laboratory conditions are confirmed by standard tests for the hardness of samples, their chemical composition and metallography. These studies confirmed the possibility of volumetric action on the material of the samples for various variants of technological schemes and made it possible to draw conclusions about the prospects of using nano-amplitude resonance oscillations of the samples in a strong uniform magnetic field of permanent magnets for strengthening the samples. It is shown that for samples of eutectoid steel with a carbon content of 0.8%, magnetic resonance treatment of the samples with an electric signal source with a power of only 3 watts for 50 minutes made it possible to achieve a change in Brinell hardness up to 35%. In this case, the formation of a mesh of a reinforcing nature made of lamellar pearlite in the bulk of the sample material was observed. An increase in the amplitude of oscillations of the piezoelectric resonator and, consequently, of the samples leads to an increase in the hardness of the material and the duration of reaching the steady-state value of its hardness, however, the nature of such changes is extreme. The results obtained allow us to conclude that such processing is promising for increasing the wear resistance of non-regrowed cutting tool plates, for increasing the durability of elements of mechanical parts and structures. Also, it becomes possible to expand the list of technological influences on the working surfaces of machine parts, along with surface plastic deformation and heat treatment.