Анотация: The mathematical and physical models for critical modes of pneumatic conveying has been developed to ensure calculations and design of the main pneumatic product pipelines with a continuous mode of operation. The model takes into account the technological conditions of the gas suspension movement; the laws of motion of individual small-piece particles, taking into account their impact interaction and decompression, as well as real boundary conditions for the movement of a food product. The parameters of the zone of dynamic destruction of the layer of smallpiece food product by the air shock wave were experimentally investigated and the comparison of the calculation results with the experiment was performed. The process of controlling the critical modes of pneumatic conveying based on proportional elements and feedback ( current loop 4-20 mA ) was theoretically described; investigation of the process of destruction of a cluster of products using an air wave and controlled decompression. An approach to modelling pneumatic conveying systems as a whole is proposed. The total pressure loss in the pneumatic conveying pipeline is investigated, it consists of: pressure losses arising from the movement of clean air; additional pressure losses arising from the movement of material; pressure losses to maintain the transported material in suspension in a vertical section; pressure loss for acceleration of transported particles when they are drawn into the transport pipeline; which are directly proportional to the volumetric mass of air, the speed of its movement and the weight concentration of the material in the mixture