The scale-up of hydrothermal oxidation process depends on the development of simulation tools. The reaction in a supercritical water oxidation reactor which is confronted to a non-stationary conditions is unknown, because these manipulations could create irreversible damages to the reactor materials. In this way, we have proposed a new numerical program to determine the reactor comportment in these situations. This program permits to model mass flow rate variations (start or stop of the reactor, for example), a modification of the inlet temperature and the change of waste concentration. This program will be able to determine the functioning conditions (temperature, and waste concentration which can be destroyed) with any risk for an industrial installation. (C) 2004 Elsevier B.V. All rights reserved.