The effects of channel width and Lewis number on the propagation limits and flame transition between multiple flame regimes in mesoscale combustion were studied experimentally and numerically using methane and propane-air mixtures. The experimental results showed that both methane and propane-air flames have multiple flame regimes. It was also shown that there existed non-monotonic dependence of flame speeds on equivalence ratio. Moreover, the results also showed that there are two different flame transitions, a direct transition and an extinction transition, depending on the channel width, Lewis number, and flow velocity. For the first time, a two-dimensional numerical simulation was conducted to predict the transition between different flame regimes and to examine the effects of channel width, Lewis number, and flow rates. The results showed that flame stretch had a significant effect on the extinction limit and the flame bifurcation. The predicted results agreed qualitatively well with the experiment.