Certain limiting but exact solutions of the heat transport and chemical kinetic equations are combined with physical intuition to obtain an analytical solution of the ignition of a combustible material, assuming ignition to be the result of an adiabatic first order surface reaction. The derived equations are used to predict the ignition behavior of cellulose, and the results are shown to be in good agreement with published experimental ignition data on cloth. The theory is also used to analyze some published experimental ignition data on composite propellants, and the results agree with the published numerical solution of the equations used to describe the data. In general, the developed analytical solution appears to give essentially the same results and predicted ignition characteristics as this numerical solution, Some implications regarding the ignition mechanism of cellulose and the thermal surface ignition of explosives are also discussed.