Due to the different scenarios where sour gas is present, its composition can be different and, therefore, it can be exploited through different processes, being combustion one of them. In this context, this work deals with the oxidation of CH4 and H2S at different pressures and under a wide variety of conditions. The oxidation has been evaluated experimentally in two different flow reactor set-ups, one working at atmospheric pressure and another one operating from atmospheric to high pressures (40 bar). Different CH4/H2S mixtures have been tested, together with different oxygen concentrations and in the temperature range of 500–1400 K. The experimental results obtained show that the oxidation of the CH4/H2S mixtures is shifted to lower temperatures as pressure increases, obtaining the same trends at atmospheric pressure in both experimental set-ups. H2S oxidation occurs prior to CH4 oxidation at all conditions, providing radicals to the system that promote CH4 oxidation to lower temperatures (compared to neat CH4 oxidation). This effect is more relevant as pressure increases. H2S oxidation is inhibited by CH4 at atmospheric pressure, being more noticeable when the CH4/H2S ratio is higher. At higher pressures, the H2S conversion occurs similarly in the absence or presence of CH4. The experimental results have been modeled with an updated kinetic model from previous works from the literature, which, in general, matches well the experimental trends, while some discrepancies between experimental and modeling results at atmospheric pressure and 40 bar are found in the conversion of H2S and CH4.