A review of recent research in the field of vibration separation of bulk media has been done. It was found that the productivity of the separation process is influenced not only by the design characteristics of the vibrating separator, in particular the length, angle and capacity of the working housing, but also the dynamic processes that occur in bulk medium during separation. The efficiency of the separation process significantly depends on the mutual influence of the velocity of the bulk medium along the separator sieve and its amplitude-frequency characteristics. Based on the review, the relevance of further study of these parameters was established. Using the methods of nonlinear mechanics, a mathematical model of the motion of the layer of bulk medium on the sieve of the vibrating separator was built. The layer of bulk medium was modeled by an elastic beam, which is in contact elastically, rigidly, or as hinged. Graphical dependences of the influence of the frequency of external perturbation and the velocity of the bulk medium along the sieve of the separator on its oscillation amplitude were obtained. The obtained mathematical model and graphical dependences showed that small velocities of the medium layer lead to an increase in the amplitude of oscillations of the bulk medium and a decrease in its frequency of oscillations, which increases the permeability of medium particles and increases the productivity of the separation process. The obtained researches allow us to increase the efficiency of the separation process, to regulate the processes that take place in the bulk medium and to increase the speed of its passage through the sieve openings. The constructed mathematical model can serve as a basis for further studies of the influence of changes in the physical and mechanical characteristics of the bulk medium on its dynamic parameters in the process of vibration separation.