The article presents the formation of physical models of fittings of ventilation systems in the conditions of change of linear sizes and forms of adjacent sections of air ducts of ventilation systems. The aim is to minimize waste materials in the manufacture and sale of pipe billets of different diameters of the ventilation system, reduce metal consumption, increase production productivity and efficiency of procurement for installation of ventilation in industrial premises, identify ways to improve the installation of ventilation in industrial premises for various purposes and justification calculation methods. The use of the obtained physical models to determine the required parameters in the manufacture of sweeps of ventilation system fittings can significantly increase the efficiency criteria for procurement and installation work.