The analysis of existing methods of air classification of crushed bulk materials is carried out, priority directions of their development and improvement are identified, the hardware design of these methods and the main approaches to the calculation of air classifiers are studied. The conclusion is made about a rather isolated motion of particles in the working volume of the classifier at optimal performance. The prospects of dry separation methods and the progressiveness of creating multistage gravitational classifiers have been established. Theoretical studies of the separation process in a gravity classifier with overflow shelves have been carried out. The regularities of the process of separation of bulk materials in air classifiers have been established, reliable methods have been developed for calculating their technological and design parameters in order to create highly efficient and productive industrial plants. Theoretical dependencies and differential equations are obtained, which characterize the influence on the separation mechanism of technological and design parameters of the classifier. The results of solving the equations of motion made it possible to determine the main design parameters of the apparatus based on the technological requirements for productivity and the dispersed composition of the final products. On the basis of theoretical research, analytical relationships and differential equations have been developed that describe the separation process in a gravity classifier with overflow shelves. The use of these equations made it possible to simulate the air flow in the classifier, to obtain a field of air flow velocities for any design and technological parameters. This, in turn, shows the direction of movement of particles of different sizes or densities and makes it possible to estimate the boundary size of separation, and also allows you to study the interaction of the air flow with the material being separated in a wide range of technological and design parameters of the classifier, and, ultimately, to determine the boundary size separation and particle size range of the resulting fractions of the finished product. The relationship between technological and design parameters of the apparatus is theoretically determined.