Abstract Luminous radiation from the soot particles of a flame propagating vertically downward on a polymethyl methacrylate (PMMA) rod is investigated by using exact and approximate analyses. Investigation shows that for vertically downward burning of a 0.5 in. diam PMMA rod, the luminous radiative heat transfer from the flame to the fuel rod is well within the optically thin limit. The approximate analysis is extended to conventional hydrocarbon fuels. A simple optically thin approximation in terms of flame temperature T f and mean beam length L m is obtained for the luminous radiation from soot particles. The thin approximation gives errors of less than 5% from exact values for L m T f < 60,000 cm °K. Comparison between the present result and recent experimental data is good.