Foamed gel has begun to play an important role in permeability modification applications because of the reduced chemical requirements. Foamed gels create impermeable barriers in porous media; however, once a critical pressure differential is exceeded, the permeability increases with increasing pressure. A two-dimensional network model was developed to estimate foamed gel barrier performance in terms of the maximum pressure a barrier can withstand and the evolution of the foamed gel barrier’s permeability. The formation of conductive pathways and the accompanying permeability increase were estimated from a model of the pressure-induced deformation and rupture of individual lenses. The evolution of conductive pathways changed from invasion percolation (high elastic modulus, rigid gel) to a lens rupture chain reaction initiated by the rupture of a single lens (low elastic modulus gel) as the elastic modulus of the gel was decreased. The apparent fractal dimension of the first conductive channel ranged from 1.89 to 1.06 for high and low elastic modulus gels, respectively. This dependency of breakthrough and breakdown is unique and produces a large range of breakdown behavior for any degree of microscopic heterogeneity.