We treat the infiltration of an initially dry deformable porous medium by a pressurized liquid, taking into account the influence of variations in permeability within the deformed porous medium. Chief assumptions of our analysis are neglect of gravity, of inertial forces, and of partial saturation in the porous medium. We focus on unidirectional infiltration under constant liquid pressure, and present data from the infiltration of polyurethane sponge by ethylene glycol in a configuration of nearly unidirectional infiltration with reflief from friction effects along sample sides. We find excellent agreement between theory and experiment at longer infiltration times. We examine an additional assumption, namely the neglect of solid-phase velocity compared with average local liquid velicity at lower porous-medium strains. Agreement of this simplified model with experimental data, albeit less good, remains quite acceptable given the considerable computational simplicity it produces.