The radiolysis of porewaters by uranium, thorium, and potassium in mineral grains is a recognised source of molecular hydrogen in rock- and sediment-hosted fluids. This radiolytic hydrogen is of geomicrobiological interest as a potential energy source (electron donor) for microbial metabolism, especially in energy-limited settings such as the marine deep biosphere or the subsurface of Mars. Previous efforts to predict the production of radiolytic hydrogen from columns of rock and sediment have tended to rely upon analytic models that cannot account for the attenuation of mineral radiation by grains larger than ~30 microns. To address this, we have developed a Monte Carlo method to simulate the physics of mineral radiation and evaluate the production of H₂ as a function of mineral grain size and radioisotope composition. The results confirm that grain size is a major control on radiolytic H₂ yield. For example, using the standard geological classification of grain sizes, we find that clay can produce up to an order of magnitude more H₂ per unit time than sand. The magnitude of this effect is illustrated using compositional data from real geological units in order to demonstrate the dependence of radiolytic hydrogen flux on natural radionuclide concentration and bulk porosity.