Purpose. Clarification of the mathematical description and calculation of the processes of micronization and vibrational movement of grain in cross-air flow on the basis of experimental studies. Methods. Experimental studies were performed on a manufactured sample of a machine for high-intensity heat treatment of grain using experimental planning methods and statistical processing of experimental data. Results. A mathematical description of the motion of grain mixture particles on a vibroconveyor with high-intensity heat treatment of grain during action on the mixture of air flow is given. The trajectories of particles with different sizes depending on high-intensity heat treatment are obtained. With certain assumptions, the regularities of the change in the speed of movement and exposure of the micronization of the material particle (grain) from the coordinates and humidity are obtained. Conclusions. As a result of research: 1) a regression dependence was obtained to determine the micronization exposure and it was established that the micronization exposure for the given energy parameters of the installation should last from 60 to 180 seconds; 2) the change of the speed of vibratory movement of grain depending on its humidity is theoretically substantiated and it is proved that the ascending air flow increases the speed of grain movement, and the descending one – decreases; 3) experimentally determined the empirical dependence of changes in the speed of vibration, which allows the formation of the required speed of vibration of grain by changing the parameters: the slope of the vibrating surface 5÷8°, oscillation frequency 33÷52 s-1, grain moisture 10÷20% and downward air flow rate 0.1÷2 m / s in rational modes of installation for grain micronization on a vibrating conveyor. Keywords: trajectory, vibration displacement, vibration conveyor, air flow, micronization, humidity, coefficient of friction.