Over the last few years, vegetable oils have become an integral food part of the vast majority of the planet's population. In order to preserve all valuable substances in vegetable oils, it is necessary to correctly choose the rational parameters of the oil extraction process. The main purpose of this research is to analyze the influence of various factors on the quantitative and force parameters of the oil extraction process and substantiate the prospective directions of automation of the screw press operation. The research methodology is focused on mathematical modeling of the pressing process and analyzing the stress-strain characteristics of the pressed material (sunflower seeds and cake) at different operational conditions and design parameters of the screw. The obtained results are presented in the form of analytical dependencies of the press output (productivity), extraction pressure, and consumed power on the screw rotational frequency and screw flight pitch. The corresponding graphical dependencies are plotted for visualization of the obtained results with reference to the existing household press LiangTai LTP200. The conclusions on the prospective directions of automation of the screw press operation are drawn. Particularly, the necessity of regulating the temperature of the pressing chamber and extracted oil by means of applying additional heating and cooling devices is substantiated. As well, the sensors that monitor the mass of the extracted oil and the consumed current of the electric motor are proposed to be installed. The rotational frequency of the screw is suggested to be adjustable by applying the frequency converter controlled by the additional electronic system based on the data obtained from the sensors. The paper may be used by scientists and engineers working on designing screw presses and improvement of their performance characteristics. Further investigations on the subject of this research may be focused on experimental verification of the qualitative and quantitative parameters of the extracted oil depending on the type of the seeds or kernels to be pressed, and operational parameters of the press (screw rotation frequency, temperature of the pressing chamber, etc.).