A one-dimensional numerical model describing the physical and chemical phenomena occurring in a translucent solid fuel up to ignition is used to investigate the failure of the classical ignition theory at radiant heat fluxes above 70 kW/m(2). Comparison with a very large dataset of experimental measurements of time to piloted ignition for black PMMA (PolyMethylMethAcrylate) samples shows that model predictions agree well for heat fluxes from 20 to 200 kW/m(2). The only two available sets of experimental data for ignition at high heat fluxes for black-carbon coated and uncoated samples are used. Predictions of the transient temperature profiles inside the solid at different heat fluxes also agree well with measurements. Among all the mechanisms investigated, agreement with measurements at heat fluxes above 70 kW/m2 is only possible when in-depth radiation absorption is included in the model. Observed behaviour at high heat fluxes cannot be explained by the reaction scheme, ignition criterion, temperature dependency of material properties, surface heat losses or radiation attenuation by pyrolyzates. The model is also used to show that the traditional coating of black carbon added on the sample does not cancel in-depth radiation absorption but its effect is to absorb at the surface around 35% of the incoming radiation. The work explains the failure of the classical ignition theory at high heat fluxes and it is the first time that the effect of black-carbon coating is explained and quantified. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.