Catalytic combustion of hydrocarbon mixtures involves the adsorption of the fuel and oxidant into a platinum surface, chemical reactions of the adsorbed species, and the desorption of the resulting products. Re-adsorption of some produced gases is also possible. The catalytic reactions can be beneficial in porous burners that use low equivalence ratios. In this case, the porous burner flame can be stabilized at low temperatures to prevent any substantial gas emissions, such as nitric oxide. The present paper is concerned with the numerical computation of heat transfer and chemical reactions in flowing methane-air mixtures over a platinum coated hot plate. Chemical reactions are included in the gas phase and in the solid platinum surface. In the gas phase, 16 species are involved in 49 elementary reactions. On the platinum hot surface, additional surface species are included that are involved in 24 additional surface chemical reactions. The platinum surface temperature is fixed, while the properties of the reacting flow are computed. The flow configuration investigated here is the parallel boundary layer reacting flow. Finite-volume equations are obtained by formal integration over control volumes surrounding each grid node. Up-wind differencing is used to ensure that the influence coefficients are always positive to reflect the physical effect of neighboring nodes on a typical central node. The finite-volume equations are solved iteratively for the reacting gas flow properties. On the platinum surface, surface species balance equations, under steady-state conditions, are solved numerically by an under-relaxed linear algorithm. A non-uniform computational grid is used, concentrating most of the nodes near the catalytic surface. Surface temperatures, 1150 K and 1300 K, caused fast reactions on the catalytic surface, with very slow chemical reactions in the flowing gas. These slow reactions produce mainly intermediate hydrocarbons and unstable species. The computational results for the chemical reaction boundary layer thickness and mass transfer at the gas-surface interface are correlated by non-dimensional relations, taking the Reynolds number as the independent variable. Chemical kinetic relations for the reaction rate are obtained which are dependent on reactants’ concentrations and surface temperature.