A theoretical study is conducted of the spread of flames in gas flows moving in the direction of flame propagation. The study draws on the fact that concurrent flame spread configurations have common general characteristics, thus allowing a unified treatment of the problem. The analysis, although approximate, provides an analytic expression for the rate of flame spread over the surface of thermally thick fuels in laminar gas flow configurations that accept a similarity solution. The predicted flame spread rates for these particular flows provide limits for the rates of spread in other non-similar gas flow configurations.