Geopressuring, secondary porosity, and low-permeability zones occur in many of the world's sedimentary basins and are often associated with major petroleum reservoirs. We present a mechanical model which simultaneously reproduces these phenomena. Assuming pressure solution to be the dominant rock deformation mechanism, a solid-state rock skeleton viscosity is introduced which relates the deformation of the rock skeleton to the effective stress. Numerical solutions for compaction indicate that a soft sedimentary layer preferentially compacts to form a low-permeability zone. There is a large liquid pressure gradient through the low-permeability zone. In the more slowly compacting region beneath the low-permeability zone, the pressure gradient remains hydrostatic but the absolute pressure can exceed the lithostatic pressure in the absence of hydraulic fracturing. This results in the formation of secondary porosity. ¿ American Geophysical Union 1994