This study uses the nanoindentation technique to evaluate the mechanical properties of thin copper films at indentation depths measured in the order of nanometers. Copper films with various thicknesses are deposited on a single crystal silicon wafer with a (100) orientation and on a polymethylmethacrylate (PMMA) substrate, respectively. The experimental results show that for soft thin films on a hard substrate, the substrate effect is negligible when the indentation depth is less than 20% of the film thickness. However, the results suggest that hard films on a soft substrate should be treated as a composite system in indentation because the substrate effect is significant. Finally, the results reveal that a significant indentation size effect exists for thin films with a thickness of less than 100nm. A number of possible reasons for the depth dependence of the hardness properties at ultra-shallow indentation depths are proposed and discussed.