The infiltration of a non-wetting liquid, such as molten metal, into a porous solid, such as a ceramic preform, is influenced by the wetting angle of the liquid on the solid. The link between local wetting and the minimum pressure required for initiation of infiltration or the pressure required for full preform infiltration can deviate strongly from what one would expect on the basis of elementary thermodynamic considerations or simple geometrical models. In this work, we explain the trends observed in experimental studies of pressure infiltration of molten metal into ceramic preforms by means of a percolation model, in which the pores themselves are given a simple geometric shape. This gives a simple yet rich and realistic treatment of the infiltration process. Specifically, the pop-through pressure necessary to traverse a throat between two neighboring circular (2D) or spherical (3D) pores can easily be calculated and incorporated in a 3D network model of many pores produced by generating a packing of slightly overlapping circles or spheres. The resulting pore structure defines a bond percolation network that agrees overall both with predictions of percolation theory and observations from experiment, and which can be extended to address a range of other aspects of multi-phase flow through porous media. (c) 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.