Using nanoindentation, the elastic moduli of composite film/substrate systems of amorphous Al2O3, thin films, with the thickness ranging from approximately 3 nm (native oxide) to 300 nm on aluminum and sapphire substrates, were studied. When indenting deeper into the samples, the transition from the elastic modulus of the film to that of the substrate is found to scale with the ratio of depth of indentation to film thickness (h/t) and is described by a transitional function. The measured elastic modulus and the corresponding compliance are compared with the Doerner and Nix expression, with the parameterization of King, and with the predictions of the model of Gao et al. It is found that the measured transitional function is not a unique function applicable both to rigid/soft and soft/rigid film/substrate systems, but is sensitive to the relative mechanical properties of the film and the substrate, in contrast to the predictions of the theoretical treatments mentioned above. The comparison of the experimental results with a model based on a hydrostatic core, where the dependence of the transitional function on the relative elastic moduli of the film and the substrate is taken into account, shows a reasonable agreement.