In this work a new mathematical model of vegetable oil extraction in an industrial "De Smet" type extractor is proposed to predict the concentration distributions in percolation sections and at the outlets. Oil losses are also considered. The model incorporates counter-current crossed flow of the porous media and the miscela, mass transfer between the expanded flakes and the miscela, diffusion in the entire extraction field, miscela transport between the percolation sections, influence of loading and drainage zones, and transient operational regimes of the extractor. The model is composed of sub-models for the percolation sections, trays, drainage and loading zones. The sub-models are coupled to each other by means of the boundary conditions, and reflect the particularities of counter-current flow. The calculation algorithm is based on the method of lines. The variations in concentration distributions of bulk and pore phases, and their properties, such as: waves, slopes, steps, etc., are presented. (C) 2004 Elsevier Ltd. All rights reserved.