Vibration treatment in finishing processes is becoming a more complex technology, sometimes leading to weak shock waves occurring in the abrasive working medium. Here, the preconditions are discussed for the appearance of the effect of a shock wave of the vibrating working medium in a vibrating machine reservoir during multi-energy vibration processing. The peculiarities of the propagation of the force pulse of abrasive granules in the working medium, as in a pseudogas, are considered based on the kinetic theory of gases and the equations of gas dynamics. The paper also describes the motions of the parts in the working medium and the mechanism of the appearance of a weak shock wave, such as the compressive shock wave of abrasive granules. The interaction of the surface of the oscillating processed part with the granules of the working medium is studied. The characteristic of the Hugoniot adiabat for working medium granules is given. The influence of compression shock wave on the process of vibration processing is revealed. A comparison is made with experimental data.