The mathematical model for the process of oily raw materials pressing with single-screw oil press has been developed, which makes it possible to calculate the main design parameters of an oil press for extracting oil from oil crop seeds. This model of pressing describes the process of moving meal in the pressure zone and expression of oil in the pressing cage of the screw press, taking into account the following assumptions: porous skeleton and oil have the same density, they have no chemical interaction, the process of oil filtration occurs under isothermal conditions with laminar conditions of motion. The developed mathematical model corresponds to physical meaning of the occurring phenomena and can be used to analyze the work of active presses, and at the design stage.