In this paper, a model for spreading and sorption of a droplet on a thick porous substrate is derived in the frame of lubrication theory. Flow in the saturated part of the porous material is governed by Darcy's law, assuming a discontinuous wetting front separating the saturated from the unsaturated regions. Numerical results are presented for spreading and sorption of droplets in their dependence on the material and process parameters for axisymmetric and two-dimensional configurations. (C) 2004 Elsevier Ltd. All rights reserved.