The differential cross sections for 16O(He,He)16O resonant elastic scattering at 3.034 and 3.078 MeV have been measured using stoichiometric thin (100 Å) and thick (6000 Å) SiO2 layers formed on Si(100) wafers by thermal oxidation at 900 °C under H2 and O2 flows. We have determined the resonance widths (Γ) and interaction radii (a), which are the parameters defining the cross sections in the partial wave analysis, by best fitting the angular and energy dependent scattering yields from oxygen. A computer simulation program for Rutherford backscattering including the 16O(He,He)16O resonant scattering has been synthesized and applied to the elemental analysis of thin YBa2Cu4O8 and Nd1+xBa2-xCu3O7-δ films grown on SrTiO3 substrates. The present elemental analysis is compared with the transition temperatures of superconductivity (Tc) in the context of the oxygen deficiency. The accuracy of oxygen content is estimated to be better than 0.1 (a few %). How to improve the accuracies of the elemental analysis, in particular the oxygen content, is discussed in detail. © 1996 American Institute of Physics.