Mathematical models of compaction in sedimentary basins typically assume a relationship between effective pressure pe and porosity ϕ, which is of a non-linear type; that is, pe=pe(ϕ). However, at depths greater than a kilometer, pressure solution becomes important and this relationship approaches a viscous one. We derive a mathematical model for viscous compaction in sedimentary basins and show how the model suggests different styles of behavior in the limits of slow and fast compaction. ¿ 1999 American Geophysical Union