A new mathematical model of vegetable oil extraction in an industrial De Smet type extractor is proposed. Solvent extraction from a mobile bed of oilseed material was modeled considering different availability of oil in pellets, countercurrent cross-flow of the porous solid and the miscella, diffusion in the entire extraction field, mass transfer between pellets and miscella, miscella transport between the percolation sections, loading and drainage zones, and transient operational regime of the extractor. The mathematical model was solved numerically to predict oil concentration in miscella and pellets through the percolation sections and at the outlets. Model predictions were compared with experimental industrial data for sunflower oil extraction with hexane. Differentiation in two oil categories in terms of availability and extraction kinetics allows to represent the extraction phenomena in a better way than considering a single process. Consideration of dispersion fluxes improves the results without increasing the computing time. Saturation is reached in the stages near to loading zone when low miscella velocity is used. (c) 2007 Elsevier Ltd. All rights reserved.