A two-dimensional mathematical model of the initial stage of depth filtration is developed. This model describes the fluid flow and the particle transport and capture in a representative elementary volume of the filter. A typical simulation can be outlined as follows: as a first stage, the flow field is computed in the whole complex void space of the filter using a lattice-Boltzmann method. As a second stage, the trajectory analysis is derived by applying Newton's second law to suspended particles in the flowing fluid. The capture or the reentrainment of the particles encountering the filter surface is determined from a force balance that takes into account the drag force and the solid friction force. This approach, which provides both microscopic data such as the initial capture probability density and macroscopic data such as the filter coefficient, is validated on a model experiment of deep-bed filtration. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 39-48, 2006.