Abstract <p>Mathematical modeling methods were employed to analyze the combustion failure of cylindrical samples in a gas-free mode under conductive and radiant heat loss conditions. A method was proposed for estimating critical parameters, including critical cylinder diameter, as well as temperature and velocity at the combustion limit under non–adiabatic combustion conditions. It was shown that experimentally determined front velocities allow for the calculation of the dimensional critical cylinder radius. The influence of the multi-dimensional nature of a non-adiabatic front on critical combustion conditions was investigated.</p>