A computational study of the effect of heterogeneous radical destruction and crevices on end-wall flame quenching in a lean CH4-O2-Ar mixture at low pressure has been performed. The unsteady conservation edlaations for a chemically reacting multicomponent gas have been solved with the commercially available partial differential equation solver package PDEPACK. Heterogeneous radical destruction at a cooled surface was found to have a minor effect on flame quenching compared to homogeneous destruction in the cooled flame gases near the surface. These results are in qualitative agreement with experiments performed in a side-wall geometry. Cooled crevices, however, had a much greater effect on the postquench oxidation of the fuel. Whereas the fuel layer left after quenching near a fiat wall burns up more rapidly as the pressure is increased, unburned fuel left in a crevice after quenching burns up more slowly as the pressure is increased. This reaffirms the potential importance of crevices as sources of unburned hydrocarbons in an engine. [4], CH 4 [4], methane-ethane mixtures [5], CO [6], and H 2 [6]. Potential applications for these calculations are numerous and are well described in a recent review [3]. We have begun to develop a code to perform these calculations because of their usefulness for conducting computer experiments on such combustion phenomena as flame quenching, propagation, inhibition, ignition, and pollutant formation and destruction.