A kinetic model is developed to investigate intergranular pressure solution. This model couples stress-induced dissolution at grain contacts, diffusion through grain boundaries, and precipitation in pore spaces. The rate-controlling processes are evaluated according to the dimensionless concentrations at grain contacts and in the pore fluid. Constrained by the experimental results of creep compaction of quartz sands, calculations suggest that the equilibrium concentration at stressed grain contacts (ceqb) does not exceed 1 order of magnitude higher than the hydrostatic equilibrium concentration (ceq) at the initial stages of creep compaction. However, ceqb decays rapidly with increasing compaction and becomes close to ceq after several percent strain. The diffusivity at grain contacts is 1–2 orders of magnitude lower than the diffusivity in pore fluid. The rate-controlling process is related to grain size and strain. An increase in grain size shifts the systems toward the diffusion-controlled regime, while an increase in strain shifts the systems from dissolution-controlled regime toward either diffusion-controlled regime (larger grains) or precipitation-controlled regime (smaller grains). Intergranular pressure solution appears to be very sensitive to pore-fluid chemistry. Even a slight supersaturation in the pore fluid could prevent the diffusion along grain contacts. This may explain why the strength of intergranular pressure solution varies widely in natural sandstones.