Summary: The displacement of one incompressible fluid by another in a porous medium is studied using the network representation. The Bernoulli percolation model for an infinite lattice graph is utilized in the interpretation of the capillary behavior of the medium. The calculated capillary pressure-saturation relationship using the Bethe lattice results agree qualitatively with experimental data. It is shown that in some special cases of two-dimensional media no nonwetting phase removal is possible.