Hydraulic testing has revealed dramatic underpressures in Paleozoic shales and carbonates at the Bruce nuclear site in Ontario. Although evidence from both laboratory and field studies suggests that a small amount of gas phase methane could be present in the shale, previous studies examining causal linkages between gas phase and the underpressure have been inconclusive. To better elucidate processes in such a system, we used a highly simplified 1-D representation of the site to test, using iTOUGH2-EOS7C, the effects of various factors on the evolution of gas phase methane and pressures within the system. Heterogeneity was represented using three stratigraphic regions with distinctly different capillary pressure characteristics and, in one case, a few thin, distinct zones. Underpressure occurred only when gas pressures set as an initial conditions required it, and even in this case it was geologically short-lived. We conclude that the presence of multiple fluid phases is unlikely to explain the underpressure at the site, and suggest that the influence of gas phase methane on pore water flow is minimal. This is consistent with prior conceptualizations of the underpressured section as a thick aquiclude, in which solute transport occurs extremely slowly, bounded by aquifers of significantly higher permeability.