Two models of clay-rich sandstones are analyzed to explain the relative sensitivity of permeability to pore pressure and confining pressure. In one model the clay lines the entire pore wall in a layer of uniform thickness, and in the second model the clay is distributed in the form of particles that are only weakly coupled to the pore walls. Equations of elasticity and fluid flow are solved for both models, giving expressions for the effective stress coefficients in terms of clay content and the elastic moduli of the rock and clay. Both models predict that the permeability will be much more sensitive to changes in pore pressure than to changes in confining pressure. The clay particle model gives somewhat better agreement with data from the literature and with new data on a Stainton sandstone having a solid volume fraction of 8% clay.