The dynamics of the technological vibrating machine model, designed according to the scheme of a two-mass chain oscillatory system, is considered. To excite vibrations, two self-synchronizing inertial vibration exciters fixed on the working element are used. Self-synchronization of vibration exciters and oscillations of a vibromachine near its natural frequencies with a slowly changing mass of the processed material on the working element are investigated. To expand the frequency range of the oscillatory system stability, an elastic element (an elastic vibration limiter) is used, installed with a clearance between the working element and the second movable mass. The interaction of the working element with the processed material is taken into account by an additional mass and a dissipative element. On the basis of numerical simulation, it has been established that the introduction of an elastic limiter leads to a significant expansion of the frequency range near the second resonant frequency, in which the synchronous antiphase rotation of vibration exciters required for the normal operation of the machine is realized. It has been established that due to the expansion of the operating frequency range, the working element vibrations excitation with higher amplitudes is provided. In addition, in this frequency range, the oscillation amplitudes are practically independent of the processed material mass, and their magnitude can be adjusted by the initial clearance between the limiter and the working element.