Analysis of heat and mass transfer in a burning vertical surface exposed to a fluid flow parallel to the surface is presented. The combustion process considered is steady and the burning surface is in equilibrium vaporization. A fast gas phase reac- tion is assumed to occur between the fuel and the oxidizer. The flame sheet approximation is used to describe the reacting flow. The governing equations describing the conservation of mass, momentum, energy, and species concentrations were solved nu- merically along with appropriate boundary condi- tions. Schvab-Zeldovich variables were used to eliminate the mass and energy generation terms from the governing equations. Calculations were done for two different fuels and for a range of Rey- nolds number. Computed results included the distri- butions of velocity components, enthalpy, and con- centration of fuel, oxidizer, products, and inert gas, and the position of the flame sheet.