Recent results of **1**8O tracer experiments on thermal oxidation of Si in dry O//2 suggest two oxidizing species are responsible for the growth of SiO//2. We examine here a model that reflects these mechanisms in the growth rate, using a sum of two linear-parabolic growth rates. The model gives very close fits to the oxidation kinetics data for oxides ranging from 30 Angstrom to 1 mu m thick and for temperatures from 800 degree to 1200 degree C at both (100) and (111) Si orientations. Only three parameters are necessary in this model to provide excellent fits to the experimental data. A parallel diffusion of O//2 and another undetermined species is consistent with the result.