On the example of a single-mass vibrating machine with a bilinear characteristic of elastic system and inertial excitation, the article examines the possibility of forming polyharmonic oscillations close to optimal ones by exciting sub- and superharmonic resonances. A dynamic scheme of a horizontal type vibrating machine is considered, under the assumptions usually accepted in vibration technology, its mathematical model is formed and its dynamics is studied. In the frequency ranges where sub- and superharmonic resonances can be excited, the amplitude-frequency characteristics of displacements and accelerations are constructed. They are used to detect the frequencies of the driving force, at which the spectrum of steady-state oscillations are close to optimal. Stationary modes of motion are determined and compared with the desired ones. In the subharmonic resonance zone of the order of 1:2, opportunity of forming oscillations that are qualitatively close to optimal is established. The possibility of their excitation for minor disturbing forces is noted, with use of the Poincare mapping and by constructing the orbits of the initial points from vicinity of origin their stability is studied.