Catalytic combustion of hydrogen–air boundary layers involves the adsorption of hydrogen and oxygen into a platinum coated 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 and catalytic reactors 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 nitrogen oxides. The present paper is concerned with the numerical computation of heat transfer and chemical reactions in hydrogen–air mixture boundary layers that flow over platinum coated hot plates and inside rectangular channels. Chemical reactions are included in the gas-phase as well as on the solid platinum surface. In the gas-phase, eight species are involved in 26 elementary reactions. On the platinum hot surface, additional surface species are included that are involved in 16 additional surface chemical reactions. The platinum surface temperature distribution is prespecified, while the properties of the reacting flow are computed. The flow configurations investigated in the present paper are those of a flat plate boundary layer and a rectangular channel reacting flow. Finite-volume equations are obtained by formal integration over control volumes surrounding each grid node. Hybrid differencing is used to ensure that the finite-difference coefficients are always positive or equal to zero to reflect the real 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. A nonuniform computational grid is used, concentrating most of the nodes in the boundary sub-layer adjoining the catalytic surface. For the flat plate boundary layer flow, the computed OH concentration is compared with experimental and numerical data of similar geometry. The obtained agreement is fairly good, with differences observed for the location of the peak value of OH. Surface temperature of 1170 K caused fast reactions on the catalytic surface in a very small part at the leading edge of the catalytic flat plate. The flat plate computational results for heat and mass transfer and chemical surface reactions at the gas-surface interface are correlated by nondimensional relations. The channel flow computational results are also compared with recent detailed experimental data for similar geometry. In this case, the catalytic surface temperature profile along the *x*-axis was measured accurately and is used in the present work as the boundary condition for the gas-phase energy equation. The present numerical results for the gas temperature, water vapor mole fraction, and hydrogen mole fraction are compared with the corresponding experimental data. In general, the agreement is very good especially in the first 105 mm. However, some differences are observed in the vicinity of the exit section of the rectangular channel.