An analytical model for flame stabilization in meso-scale channels is developed by solving the two-dimensional partial differential equations associated with heat transport in the gas and structure and species transport in the gas. It improves on previous models by eliminating the need to assume values for the Nusselt numbers in the pre and post-flame regions. The effects of heat loss to the environment, wall thermal conductivity, and wall geometry on the burning velocity and extinction are explored. Extinction limits and fast and slow burning modes are identified but their dependence on structure thermal conductivity and heat losses differ from previous quasi one-dimensional analyses. Heat recirculation from the post-flame to the pre-flame is shown to be the primary mechanism for flame stabilization and burning rate enhancement in micro-channels. Combustor design parameters like the wall thickness ratio, thermal conductivity ratio, and heat loss to the environment each influence the flame speed through their influence on the total heat recirculation. These findings are used to propose a simple methodology for preliminary micro-combustor design. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.