Strong fluid underpressures have been detected in Paleozoic strata in the eastern Michigan Basin, with hydraulic heads reaching ~400 m below land surface (~4 MPa underpressure) and ~200 m below sea level in strata where unusually low permeabilities (~10⁻²⁰–10⁻²³ m²) were measured in situ. Multiple glaciations, including three with as much as 3 km of ice cover at the site in the last 120 ka, suggest a causal link with the underpressures. We examined this possibility using a one-dimensional groundwater flow model incorporating mechanical loading from both ice weight and lithospheric flexure. Because hydrologic and mechanical changes during glaciation are not well characterized and subsurface properties are imperfectly known, the model was used inversely to estimate flexural loads and loosely constrained permeabilities by matching observed pressures. Acceptable matches were obtained for a surprisingly wide range of scenarios with permeabilities close to measured values and plausible flexural loads. Matches were not obtained when too many parameters were preselected, or when permeabilities were constrained to be significantly larger than measured values. In successful model runs groundwater expulsion under glacial-mechanical loads caused the underpressuring, and flexural loads were important if aquifer and sub-glacial pressures were significantly elevated during glaciation. Simulated fluid pressures in the low-permeability strata fluctuated by 30–40 MPa during glacial cycles but resulted in advective transport of only tens of meters or less. Although other mechanisms cannot be ruled out, we conclude that glacial-mechanical forcing of a water-saturated system can explain the observed underpressures.