A stationary flame is stabilized in a two‐dimensional channel in such a way that it closely corresponds to the case of a flame propagating in a channel. The entire flow field of unburned and burned gases is mapped by taking stroboscopic photographs of small particles suspended in the combustible gases. The asymptotic flow field of the burned gases is analyzed in terms of flow conditions at the flame. The possibility of obtaining an analytic flow field on the basis of constant flame speed is examined. It appears that no solution exists unless the channel walls in the region of burned gases are displaced inward. This investigation, together with the previous work on the flow field of a Bunsen flame, leads to some general remarks about the structure and stability of laminar flames. The various predictions are in agreement with experiments. In particular, the convex flames are possible and concave ones impossible within the framework of the theory based on constant flame speed.