Abstract Spheroidal weathering, a common mechanism that initiates the transformation of bedrock to saprolite, creates concentric fractures demarcating relatively unaltered corestones and progressively more altered rindlets. In the spheroidally weathering Rio Blanco quartz diorite (Puerto Rico), diffusion of oxygen into corestones initiates oxidation of ferrous minerals and precipitation of ferric oxides. A positive ΔV of reaction results in the build-up of elastic strain energy in the rock. Formation of each fracture is postulated to occur when the strain energy in a layer equals the fracture surface energy. The rate of spheroidal weathering is thus a function of the concentration of reactants, the reaction rate, the rate of transport, and the mechanical properties of the rock. Substitution of reasonable values for the parameters involved in the model produces results consistent with the observed thickness of rindlets in the Rio Icacos bedrock (≈ 2–3 cm) and a time interval between fractures (≈ 200–300 a) based on an assumption of steady-state denudation at the measured rate of 0.01 cm/a. Averaged over times longer than this interval, the rate of advance of the bedrock–saprolite interface during spheroidal weathering (the weathering advance rate) is constant with time. Assuming that the oxygen concentration at the bedrock–saprolite interface varies with the thickness of soil/saprolite yields predictive equations for how weathering advance rate and steady-state saprolite/soil thickness depend upon atmospheric oxygen levels and upon denudation rate. The denudation and weathering advance rates at steady state are therefore related through a condition on the concentration of porewater oxygen at the base of the saprolite. In our model for spheroidal weathering of the Rio Blanco quartz diorite, fractures occur every ∼ 250 yr, ferric oxide is fully depleted over a four rindlet set in ∼ 1000 yr, and saprolitization is completed in ∼ 5000 yr in the zone containing ∼ 20 rindlets. Spheroidal weathering thus allows weathering to keep up with the high rate of denudation by enhancing access of bedrock to reactants by fracturing. Coupling of denudation and weathering advance rates can also occur for the case that weathering occurs without spheroidal fractures, but for the same kinetics and transport parameters, the maximum rate of saprolitization achieved would be far smaller than the rate of denudation for the Rio Blanco system. The spheroidal weathering model provides a quantitative picture of how physical and chemical processes can be coupled explicitly during bedrock alteration to soil to explain weathering advance rates that are constant in time.