The influence of air humidity on flame propagation in mixtures of hydrofluorocarbons (HFCs) with air was studied through numerical simulations and comparison with measurements from the literature. Water vapor added to the air in mixtures of fluorine rich hydrofluorocarbons (F/H ≥ 1) can be considered as a fuel additive that increases the production of radicals (H, O, OH) and increases the overall reaction rate. The hydrofluorocarbon flame is typically a two-stage reaction proceeding with a relatively fast reaction in the first stage transitioning to a very slow reaction in the second stage which leads to the combustion equilibrium products. The transition to the second stage is determined by the consumption of hydrogen-containing species and formation of HF. Despite a relatively small effect of water on the adiabatic combustion temperature, its influence is significant on the reaction rate and on the temperature increase in the first stage of the combustion leading to the increase in burning velocity. The main reaction for converting H2O to hydrogen-containing radicals and promoting combustion is H2O + F = HF + OH, as demonstrated by reaction path analyses for the fluorine rich hydrofluorocarbons R-1234yf, R-1234ze(E), and R-134a (F/H = 2). The calculated burning velocity dependence on the equivalence ratio ϕ agrees reasonably well with available experimental measurements for R1234yf and R-1234ze(E) with and without the addition of water vapor. In agreement with experimental data, with water vapor, the maximum of burning velocity over ϕ is shifted to the lean mixtures (near ϕ = 0.8).