We present a mathematical model that quantifies the rate of water radiolysis near radionuclide-containing solids. Our model incorporates the radioactivity of the solid along with the energies and attenuation properties for alpha (α), beta (β), and gamma (γ) radiation to calculate volume normalized dose rate profiles. In the model, these dose rate profiles are then used to calculate radiolytic hydrogen (H2) and hydrogen peroxide (H2O2) production rates as a function of distance from the solid–water interface. It expands on previous water radiolysis models by incorporating planar or cylindrical solid–water interfaces and by explicitly including γ radiation in dose rate calculations. To illustrate our model’s utility, we quantify radiolytic H2 and H2O2 production rates surrounding spent nuclear fuel under different conditions (at 20 years and 1000 years of storage, as well as before and after barrier failure). These examples demonstrate the extent to which α, β and γ radiation contributes to total absorbed dose rate and radiolytic production rates. The different cases also illustrate how H2 and H2O2 yields depend on initial composition, shielding and age of the solid. In this way, the examples demonstrate the importance of including all three types of radiation in a general model of total radiolytic production rates.