This paper presents the first detailed numerical study of the extinction of methane-air counterflow diffusion flames by the super-effective agent iron pentacarbonyl. Calculations using a gas-phase chemical mechanism reproduce the magnitude of inhibition for small amounts of inhibitor in the air, but over predict the inhibition effect for larger amounts of inhibitor. Reaction pathway and reaction flux analyses show that a catalytic cycle involving FeO, Fe(OH)2, and FeOH is primarily responsible for catalytic recombination of H atoms which produces the inhibition, and that a new cycle involving Fe(OH), FeOOH and Fe(OH)2, has a minor role. Reaction flux calculations demonstrate that the fractional flux of H and 0 atoms through the iron reactions increases as inhibitor concentration increases, but eventually the fractional fluxes level off. Saturation of the catalytic cycles can partially explain the diminishing effect of the inhibitor at high inhibitor loading shown in both the calculated and experimental results. Flame structure calculations are used to determine the reasons for stronger inhibition for air-side addition of the inhibitor than for fuel-side. Simulations using a idealized inhibitor confirm the important role of transport in inhibition of counterflow diffusion flames.