A physical model of solid-liquid expression from liquid containing plant materials is presented in one-dimensional (1-D) formulation. The layer of sliced cellular material is conceptualized as a double porosity system with extraparticle and intraparticle networks for liquid flow. Filtration-consolidation equations with corresponding initial and boundary conditions were formulated for both extraparticle and intraparticle networks. It was supposed for the sliced plant material that the extraparticle network forms the first porosity with low-storage capacity, while the intraparticle network forms a second porosity with high storage capacity. Computational modeling of pressure profiles in macro- and micropores versus time for different layer sections was done for real plant material (sugar beet tissue) with two different compressibility-permeability characteristics corresponding to different degrees of tissue disruption. Results demonstrate the delayed pressure drop in the intraparticle network and retardation of consolidation kinetics for the less destroyed plant tissue. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4762-4771, 2013