This paper presents the first detailed numerical calculations of the structure of carbon monoxide-hydrogen-oxygen-argon flames inhibited by CF3H. Numerical solution of the equations of mass, species, and energy conservation are performed using a chemical kinetic mechanism recently developed at the National Institute of Standards and Technology. The calculated burning velocities are compared with a set of previously published experimental measurements performed by another laboratory which encompass a range of equivalence ratios and argon, hydrogen, and inhibitor mole fractions with corresponding burning velocities of 21 to 199 cm/s. The effects of the inhibitor on the species profiles for the major products, radicals, and fluorinated compounds are determined, and the major reaction pathways for consumption of the inhibitor are discussed. The previously published experimental burning velocities are in good agreement with the results of the present calculations for most of the conditions tested. For those conditions (high fluorine-to-hydrogen ratio in the reactants) where the disagreement is largest, the rate expressions which most influence the burning velocity have been identified. The modeling results indicate that in CO flames (in contrast to hydrocarbon flames) oxygen atom reaction with the inhibitor and inhibitor fragments is a major decomposition pathway, especially when there is a high fluorine-to-hydrogen ratio in the reactants.