The use of insects as raw materials for the production of feed additives is becoming an increasingly relevant and promising area of research. Nevertheless, this area requires numerous studies, including theoretical ones. The article presents the results of research on mathematical modeling of the process of obtaining feed additives in the form of fat and protein from the larva of the Black soldier fly (Hermetia illucens) in a screw press. Mathematical models have been obtained that allow theoretically determining the productivity of a screw press and its energy intensity in the processing of insect biomass. The models are based on the Navier–Stokes equation and Darcy’s law and take into account the design and kinematic parameters of the screw press and the rheological properties of the biomass of the face and the resulting fat.