The compaction of shales or other fine-grained compressible rocks is described by a mathematical model, and specific solutions are presented graphically. The model treats the presented graphically. The model treats the upward and downward movements of the water the solid matrix in very extensive, uniform, flat-lying units. It may readily be adapted treat the compaction of sands. The principal elements of the model are: (1) continuity equations for the water and solid matrix; (2) Darcy's law; (3) an expression for the fluid potential; (4) an equation for the total vertical stress; (5) an empirical relationship between porosity and the difference between the total vertical stress and the fluid pressure; and (6) an empirical relationship between permeability and porosity. From these elements an expression is derived for the porosity within the unit in terms of the space and time coordinates and boundary conditions, for the approximation that the densities of the water and the solid matrix are constant. Numerical solutions for the fluid pressure, the total vertical stress, the pressure, the total vertical stress, the porosity, the permeability, and the velocities porosity, the permeability, and the velocities of water and solid matrix were obtained as profiles through the unit at close time intervals, profiles through the unit at close time intervals, and representative results are displayed. The events followed are: (1) shale sedimentation; (2) a time lapse following shale sedimentation; (3) sedimentation of a normally pressured unit over the shale unit; and (4) a final time lapse with no sedimentation. Two boundary conditions for the base of the shale unit are considered: (1) the underlying unit is impermeable, and (2) the underlying unit is a normally pressured sand. In the latter case, water flows both upward and downward out of the compacting unit. The solutions show that pore water pressures much greater than normal are obtained and may persist for tens or hundreds of millions of years. It is also found that a shale unit rapidly buried beneath a thick normally pressured sand develops a zone near the sand-shale boundary of reduced porosity and permeability in which the pore water pressure permeability in which the pore water pressure gradient is very large. Introduction: The presence of low density overpressured shales or mudstones in a sedimentary sequence influences the operations of petroleum exploration, drilling and production. During the exploration phase such low density fine-grained rocks influence the interpretation of seismic and gravity surveys. During the drilling of prospects, the mud casing and log programs and prospects, the mud casing and log programs and safety are affected by high pressures. During production, the possible influx of shale water production, the possible influx of shale water requires investigation.