Naturally transient flow (NTF) occurs when a groundwater regime fails to accommodate geologic changes. This paper describes a conspicuous NTF signature entirely within a low-permeability shale in an eroded basin. Flow in the shale appears to be a lagging hydrodynamic response to mechanical rebound and colling from erosion; careful, long-term measurements revealed a consistent pattern of low hydraulic head with the minimum within the shale. Available data are sufficient to rule out alternate causes of the pressure regime, and to construct a meaningful quantitative model of the effects of erosion. The shale behaves as a Kelvin substance in tests, but theoretical considerations suggest that its deformation during erosion mimics elastic behavior, permitting the model to be based on poroelasticity. Pressure patterns similar to that observed can be produced by incorporating into the model independent estimates of the shale's hydraulic, mechanical, and thermal properties and a reconstruction of the area's erosion history. The results confirm that local permeability is between 10-21 and 10-20 (hydraulic conductivity between 10-14 and 10-13 m/s), in contrast to the higher regional permeability of 2¿10-16 m2 (hydraulic conductivity of 2¿10-9 m/s) determined in an earlier study. Exploration techniques employed in this study could reveal similar NTF regimes in the future. ¿ American Geophysical Union 1993