This article is devoted to modeling the pressing process of an experimental screw press for safflower oil production in small enterprises of the grain processing industry. The theoretical analysis for developing the process of oil pressing in a screw press is considered. Using methods of mathematical modeling, the problem of squeezing the liquid phase from dispersed material is described and solved. The basic scheme and characteristics of the press equipment and the principle of its work are presented. The proposed method of the theoretical calculation of the pressing process helps to determine the optimal parameters and to press safflower oil using the proposed design of the screw press. During the process of pressing, the highest value of oil yield is reached at the diaphragm gap of δ = 0.1 mm and screw rotation speed of ω = 6.2 rad/s.