The Deal-Grove model of thermal oxidation kinetics is adapted to cylindrically symmetric mesa structures and applied to study steam oxidation of AlAs. Oxidation process parameters are extracted from available experimental data as functions of temperature and the AlAs layer thickness. The oxidation rate is found to be very sensitive not only to temperature, but also to the oxidation front position inside the mesa. The oxidation rate slows down as the oxidation front moves into the mesa, reaches a minimum, and then accelerates at the final stages of the oxidation process. Complex nonmonotonic dependence of the oxidation process on layer thickness is also revealed.