The formulation and the numerical solutions of laminar flame spreads over thin solids in low-speed concurrent flows are presented. Flame structure, solid profiles and dominant heat transfer modes will first be discussed for a two-dimensional flame in an unbounded domain. Extinction limits are investigated as a function of flow velocity and ambient oxygen percentage. Particular attention is given to the importance of flame and surface radiation and their effects on extinction limits. Flame spread in a flow tunnel is then investigated. By varying the tunnel height and tunnel wall radaitive properties, the effects of flow confinement and flame-fuel radiative interaction are delineated. Although most of the results are for two-dimensional flames, several computed results will be given to illustrate the effect of three dimensionality in a realistic flow tunnel.