Shales are the most abundant class of sedimentary rocks, distinguished by being very fine-grained, clayey, and compressible. Their physical and chemical properties are important in widely different enterprises such as civil engineering, ceramics, and petroleum exploration. One characteristic, which is studied here, is a systematic reduction of porosity with depth of burial. This is due increases in grain-to-grain stress and temperature. Vertical stress in sediments is given by the overburden less the pore fluid pressure, σ, divided by the fraction of the horizontal area which is the supporting matrix, (1−φ), where φ is the porosity. It is proposed that the fractional reduction of this ratio, Λ, with time is given by the product of φ4m/3, (1−φ)4n/3, and one or more Arrhenius functions Aexp(−E/RT) with m and n close to 1. This proposal is tested for shale sections in six wells from around the world for which porosity-depth data are available. Good agreement is obtained above 30–40 °C and fractional porosities less than 0.5. Single activation energies for each well are obtained in the range 15–33 kJ/mole, close to the approximate pressure solution of quartz, 24 kJ/mol. Values of m and n are in the range 1 to 0.8, indicating nearly fractal water-wet pore-to-matrix interfaces at pressure solution locations. Results are independent of over- or under-pressure of pore water. This model attempts to explain shale compaction quantitatively. For the petoleum industry, given porosity-depth data for uneroded sections and accurate activation energy, E, paleo-geothermal-gradient can be inferred and from that organic maturity, indicating better drilling prospects.