A detailed chemically reacting flow model was developed to study the full-fledged combustion of an initially oxide-free boron particle in a quiescent environment of combustion products. In the model, a surface chemistry mechanism previously developed for fluorine-free environments was extended to include fluorine. The effect of fluorine concentration as well as ambient gas temperature and particle size on burning rates was studied under diffusive-and chemical kinetically controlled conditions. In order to determine the dominant surface reactions, a sensitivity analysis was performed. Model results indicate that: (1) the addition of fluorine shifts the main products from B2O3(g) and HOBO(g) to OBF(g) and BF3(g); (2) for ratios of fluorine to oxygen atoms (F/O) less than 1, the kinetically controlled burning rate decreases slightly, while the diffusive-controlled burning rate decreases significantly with increasing F/O ratio; (3) for F/O ratios greater than 1, the kinetically controlled burning rate increases with F/O ratio,while the diffusive-controlled burning rate is insensitive to F/O ratio; and (4) the surface reactions of B2O3(g), O-2(g) and F(g) are found to be the rate-controlling surface reactions with the relative importance of these processes dependent on F/O ratio.