This contribution reports experimental measurements of the oxidation of H2S and CH3SH, under atmospheric pressure in a jet-stirred reactor (JSR), in the temperature range of 600–1100 K and for stoichiometric and oxidizing conditions. We update a recent kinetic model, originally developed based on the measurements of oxidation of H2S and CH3SH in a tubular flow-reactor and apply it to simulate the experimental data. The CH3SH subset of the kinetic model features new reactions based on a recent theoretical work and the rate parameters proposed in the present investigation. The oxidation of CH3SH proceeds mainly through an intersystem crossing process that leads to the formation of sulfine (CH2SO). The unimolecular decomposition of CH2SO in two competing reactions produces CO + H2S and COS + H2. The results from the model concur well with the experimental measurements, both from the present work and from the literature. We demonstrate that, both H2S and CH3S exhibit a similar ignition temperature, due to the initiation step that involves the abstraction of H initially bonded to sulfur. It is expected that, the results from the present investigation find application in processing of sour gas, including shale gas, especially in the direct combustion of the gas (i.e., without purification) for energy production.