We establish a mathematical model for the ignition of a thermally thin polymeric material in the Cone Calorimeter (autoignition mode). The model contains equations for solid phase and gas phase variables, and the two phases are coupled nonlinearly. Of particular importance are the couplings through convective and radiative heat transfer. We use the model to evaluate the critical heat flux required for ignition and identify features of the model which require further experimental validation. © 1995, Taylor & Francis Group, LLC. All rights reserved.