Premixed flames, stabilized near the outflow interface of a ceramic-foam surface burner are sensitive to flash-back into the foam, when applied in high-temperature combustion systems. This instable phenomenon is studied numerically for methane/air flames. The analysis is based on stationary and instationary computations using a 1D numerical model, solving the conservation equations for a premixed flame interacting with a solid phase, taking into account complex chemistry and radiation inside the foam. It is shown that stabilization on top of the foam is impossible for a range of velocities if the radiation temperature of the environment becomes too large. A deeper stabilization induces a large increase in the effective burning velocity and as such a higher convective heat flow. When this convective heat production can not be compensated anymore by the increasing radiative heat loss of the foam to the environment, the flame becomes unstable, leading to instationary heating of the foam and flame movement inside the material. Stabilization plots are presented from which the flash-back regions can be determined. (C) 2003 The Combustion Institute. All rights reserved.