Hydrothermal oxidation is an efficient and clean way for the treatment of wastewater containing organic matter. The purpose of this work is to develop a mathematical model of a reactor for hydrothermal oxidation. This reactor is horizontal and tubular and is designed with multi-injection points of oxidant. Its diameter is very small with regard to its length. The mathematical model is based on the plug flow assumption. The governing equations are: momentum, mass, species, and energy balances. Thanks to this model, the profiles of temperature, and concentration of chemical species are computed along the reactor. The numerical predictions of the model are compared to experimental profiles obtained in the case of supercritical oxidation of methanol. These comparisons show very good agreement.