The motion and interaction of discrete bubbles in porous materials is studied numerically using a network model. The goal is to extend analytical results for the motion of bubbles through a single straight tube to a more ``realistic'' geometry for porous materials, modeled here as a planar network of straight tubes of different radii. The problem is characterized by two dimensionless parameters, the Capillary number (Ca) and the volume fraction of bubbles (phi); results are characterized by determining the effective permeability of the network and the mean residence time of bubbles in the material. The simulations indicate that at low volume fraction most of the bubbles follow a limited number of high-flow pathways through the network. In this case the predictions of our simulations can be approximated by a simple analytical model. Bubbles interact with each other because their presence changes the local resistance to flow in individual tubes. As phi increases, interactions between individual bubbles become important resulting in a wider range of mean residence times in the porous material.