When miniaturizing catalytic combustors from the macro- and meso-scale down to the micro-scale, some phenomena start playing a relevant role, such as heat losses toward the external environment and transverse diffusion with respect to the residence time. These phenomena may significantly affect the thermal behavior of catalytic micro-reactors. In this work, three-dimensional computational fluid dynamics (CFD) simulations are run for studying the effect of the cross-sectional geometry on the ignition/extinction behavior of catalytic micro-combustors. Two different shapes of the cross-section are investigated, circular and square. Stability maps are built and compared for lean propane/air combustion at different inlet gas velocities. Results demonstrate that, at low inlet velocities, the square cross-section channel is more resistant to extinction than the cylindrical channel. Furthermore, it is shown that, close to the ignition point, a strong coupling between fluid flow and superficial reaction rate is established. For both geometries, this coupling does not allow blowout to occur when increasing the inlet velocity up to the value limiting the laminar regime for the incoming flow. (C) 2009 Elsevier B.V. All rights reserved.