Effects of radiative heat transfer on the behavior of a laminar diffusion flame over a solid combustible are explored. The theoretical model includes the two-dimensional Navier-Stokes momentum, energy and species equations with a single-step overall chemical reaction and second-order, finite-rate Arrhenius kinetics. A solution strategy, called the discrete ordinates method, is employed to calculate the radiation source term. Numerical studies are performed over a wide range of mass absorption coefficients characterizing the radiation absorption and emission of fuel vapor gas. When the radiation absorption is significant, radiative heat loss retreats flame downstream over the fuel surface causing the shrinkage of size and diminution of maximum temperature. It is inferred that thermal radiation may be the controlling mechanism of diffusion flame stabilization and thus neglecting radiation can cause errorneous prediction on the flame behavior and structure in combustion reaction processes. Results on the effects of wall emissivity are also presented.