A one-dimensional two-phase mathematical model of an ideal plug-flow reactor for methane air conversion on a Ni–MgO monolith catalyst on porous nickel was proposed. The model describes the methane air conversion as the result of three simultaneous reaction stages: methane deep oxidation, methane steam reforming, and reverse shift reaction. The effect of the external gas–solid mass transfer is taken into account in two variants: (i) independent diffusion and (ii) multicomponent diffusion for all mixture components. The results of modeling were used to analyze the experimental data (obtained in our previous work) on the dependence of the temperature of the front layer of the catalyst on the pressure and excess air coefficient. The best agreement between the calculation and experiment was obtained under conditions of complete external diffusion control of the exothermic stage for oxygen and the transition (between the kinetic and external diffusion) region of the endothermic stage, the kinetic effect of the endothermic stage being further limited by internal pore-diffusion resistance of the rate of this stage for methane.