Abrasive flow machining is one of the promising technologies for finishing rectangular channels, which are characterized by a constant increase in accuracy and reduction of surface roughness. During modeling of the contact interaction of grains in the corners of rectangular part cross-section in the intended abrasive flow machining, the key features of the size and filler grain selection were fixed. In the proposed spherical grain model, the cutting edge is represented by an arc of a circle that fits into the angle of the cross-section of the part. It is confirmed that if the grain size exceeds the value of the inner radius of the rounded corner of the part, an untreated zone appears, with the area calculated using the CAD system on a straight, blunt and sharp angle. It is proved that the abrasive flow machining with a filler grain size not exceeding the value of the doubled radius of the inner rounding of the rectangular cross section is carried out. The physical properties, the shape of the cutting edges and the applicability of fillers, electrolytically produced corundum, silicon carbide and synthetic diamond were analyzed. The shape of a diamond grain, in comparison with the fillers mentioned above, shows a more rounded shape of the crystal faces, which causes greater microhardness and abrasive ability. The revealed features confirm the exclusion of a possible phenomenon, caricature in the process of post-processing. It is recommended to use abrasive grains of a certain grain size for uniform pretreatment of a rough surface, followed by polishing with an ointment-like diamond paste of channels of small transverse rectangular cross-section. Using as a filler a salve-like paste containing diamond grains allows to reduce medium viscosity and machining corners of rectangular section. Abrasive flow machining with medium viscosity with synthetic heat-resistant rubber as the base and a salve-like paste containing diamond grains is used for finishing machining of non-ferrous parts. The use of working media with diamond pastes will allow the internal channels of blanks made of various non-ferrous alloys to be treated with an abrasive flow. For the minimum cross sections of rectangular pipe blanks presented in this article, it is proposed to use the working medium of the following weight composition: synthetic heat-resistant rubber - 40 %, salve-like diamond paste ASN 60/40 PTO - 60 %. A number of general recommendations are proposed for further research.