Abstract The theory to predict ignition of solid fuels exposed to incident radiant heat fluxes has permitted to obtain simple correlations of the ignition delay time with the incident heat flux which are useful in practical engineering applications. However, the theory was developed under the assumption that radiation does not penetrate into the solid phase. In the case of semi-transparent solids, where the penetration of radiation plays an important role in the heating and subsequent ignition of the fuel, the predictions of the classical ignition theory are not applicable. A new theory for the piloted ignition of optically thin cylindrical fuels has been developed. The theory uses an integral method and an approximation of the radiative transfer equation within the solid to predict the heating of an inert solid. An exact and an approximate analytical solution are obtained. The predictions are compared with piloted ignition experiments of clear PMMA cylinders. The results indicate that for opticallythin media, the heating and ignition are not sensible to the thermal conductivity of the solid, they are highly dependent on the in-depth absorption coefficient. Using the approximate solution, the correlation 1 / t i g ∝ q ˙ i n c ″ was established. This correlation is adequate for engineering applications, and allows the estimation of effective properties of the solid fuel. The form of the correlation that was obtained is due to the integral method used in the solution of the heat equation, and does not imply that the semi-transparent solid behaves like a thermally thin material. The approximate solution presented in this article constitutes a useful tool for pencil-and-paper calculations and is an advancement in the understanding of solid-phase ignition processes.