The working process of concrete mixture compaction is investigated. The model of the processing medium is determined, which is characterized by three stages. At the first stage of compaction it is a free-flowing medium, at the second and third stages of compaction it is an elastic-viscoplastic medium. This result lies in the definition of the physical and mathematical model, the equations of motion. The vibration system «machine-medium» at any moment of movement consists of two components -one is capable of accumulating energy that passes from one form to another (reactance), and the second is energy dissipation (active resistance). The influence of active and reactive forces on the general movement of the system under study has been investigated and determined. By solving the equations, analytical dependencies were obtained, which established the laws of motion of the «Vibration machine -sealing medium» system. Practical implementation for technical systems for the formation of concrete products and soil compaction processes under the main pipeline has been carried out. An algorithm and method for calculating the main parameters of vibration systems for compaction of working media have been developed.