Pressure solution and the subsequent precipitation of the dissolved material may play an important role in the lithification of sandstones and limestones. This paper presents a one-dimensional model for a well-sorted quartz arenite sequence undergoing diagenesis. The sedimentary sequence is treated as a saturated porous medium in which pressure solution occurs at individual grain contacts. Quartz dissolved at grain contacts precipitates on free surfaces of adjacent grains. This solution-and-precipitation process reduces porosity and forces the migration of pore fluid. Permeability decreases with porosity, hindering fluid migration, and excess fluid pressures are generated. Distributions of porosity, pore-pressure, and fluid-flow rates are given for several sedimentation rates and thermal gradients. Complete reduction of the primary, intergranular porosity was accomplished, in all cases examined, by a depth of 3.5 km.