In this paper a nonlinear mathematical model of the kinetics of two-molecular heterogeneous catalytic reaction proceeding on a supported catalyst is investigated numerically. The model is based on the Langmuir–Hinshelwood type kinetics of the surface reactions assuming that all species are well-mixed. The effect of the catalytic surface size, adsorbtion rate constants and jump rate via the catalyst-support interface constants on the catalytic reactivity and product concentration is studied for different arrangements of the adsorption sites.