A reactor for treating with pressurized water a material in a fluid reaction medium. It comprises a body (2) delimiting a reaction area (10), an inlet (48) for the material to be treated in the reaction area (10), a point (46) for introducing an oxidant into the reaction area (10), at least one outlet for the treated material outside the reaction area (10), the material to be treated follows a path defined in the reaction area between its inlet and its outlet. The point (46) for introducing the oxidant in the reaction area (10) is located downstream from the inlet (48) for the material and is spaced apart from the latter by a certain distance so as to define an anoxic area (20) comprised between the inlet for the material to be treated and the point for introducing the oxidant, an area in which the fluid medium is in anoxia.