A model for the simulation of the combustion of a packed bed in a stagnation point flow is presented. The model is one-dimensional and couples the chemical reactions and heat and mass transport in the bed and in the adjacent flow field. The particles are assumed to be of carbon; heterogeneous solid-gas reactions in the bed as well as a homogeneous gas-phase reaction in the free flow are considered. Ignition and extinction may occur with respect to both heterogeneous and homogeneous reactions. Depending on values like the water vapor content and the oxygen content of the stagnation point flow, the ignition can lead to discontinuities in the steady-state solutions and to multiple steady states. The number of solutions also depends on whether the combustion process is controlled by a given surface temperature of the packed bed or by a given external heat flux to the surface. The flame which establishes when the gas-phase reaction ignites can detach from the surface of the packed bed simultaneously with ignition or, depending on for example the water vapor content of the free flow, at a higher value of the external heat flux.