A new explicit numerical simulation (ENS) method based on lattice-gas automata (LGA) is introduced here for the flow of solid/fluid suspensions with deposition in porous media. The ENS method explicitly resolves the dynamics of the individual solid particles and the suspending fluid in the domain defined by the pore walls and solid particle surfaces. After describing the new method, it is applied to the study of solid/fluid suspension flow with deposition in a constriction and in a model random porous solid. This study clearly demonstrates that the deposits strongly influence the local flow fields, which in turn affect the deposition process indicating that this interplay should be modelled if accurate results are desired from trajectory methods. (C) 2003 Elsevier Science Ltd. All rights reserved.