Abstract An a priori model has been developed for the prediction of the behavior of stationary flames of premixed propane and air inside a refractory tube. The model postulates plug flow with perfect radial mixing and no axial mixing, conduction, or diffusion. The gas is assumed to be transparent but radiant exchange within the tube, longitudinal conduction in the tube wall, and chemical kinetics in the gas phase are taken into account. An approximate representation for the configuration factor for radiant exchange permitted reduction of the energy and component balances to a set of ordinary differential equations which were solved numerically by a finite-difference method. The numerical solutions agree well with the previous experimental results of Chen and Churchill and of Bath for the wall temperature profile and the blowoff and flashback velocities in the range of turbulent flow. A different model is needed for tubes less than 3/8-inin diameter since laminar flow then prevails. The model is used to predict the profiles of gas temperature and conversion and the effects of feed temperature, fuel-to-air ratio, tube diameter, tube length, wall emissivity, wall conductivity, and radial heat losses on the blowoff and flashback velocities. The model suggests the existence of multiple stationary states for all conditions in the stable region.