The mathematical model for the multiphase steady-state processes on a partially-wetted porous catalyst slab in the conditions of the exothermic catalytic reaction, species diffusion, phase transitions, and capillary phenomena interaction is developed. Numerical experiment was carried out for the model reaction of alpha-methyl styrene hydrogenation. The impact of the external wetting efficiency on the steady-state regimes of the slab is investigated. The partially-wetted regime is characterised by studying the width of the dry zone inside the slab; the slab overheating, the area of the multiplicity.