Flame stability of methane/air mixtures in mesoscale channels with different diameters (6 mm, 5 mm and 4 mm) filled with fibrous porous media was experimentally investigated. Standing combustion waves (namely, stationary flame) are observed under low inlet velocity and high equivalence ratio conditions. Moreover, the standing wave regime becomes narrower as the channel diameter is reduced from 6 mm to 5 mm and vanishes for the 4-mm channel. For a fixed equivalence ratio, the flame length becomes shorter at a smaller channel or a less inlet velocity. Regarding the downstream propagating wave, its propagation velocity increases with the decrease of channel diameter. Splitting flame appears at large inlet velocities. Besides, at low equivalence ratios, the downstream propagating flames grow into small flame balls and can survive until the channel exit. Numerical results demonstrate that for a smaller channel, although the total heat loss rate is reduced, its heat loss ratio is increased, which leads to a lower wall temperature level and the flame is quenched out near the wall. The combustion efficiency is decreased significantly for the 4-mm channel due to fuel leakage from the near-wall "dead space". (C) 2016 Elsevier Ltd. All rights reserved.