The structure of interest is a thin, metallic coating of fcc copper, of thickness down to a few nanometers only, resting on a stiffer substrate. The elastic and plastic properties of the thin coating using nanoindentation under different geometrical features such as size of the indenter and coating thickness are determined. The force-displacement curve is monitored during indentation and the precise conditions for the occurrence of so called pop-ins during loading are investigated. To simulate the nanoindentation process, a molecular dynamics approach is used, where an infinitely stiff indenter is pushed into the coating under displacement control. The coating is modeled as a thin rectangular plate, with the bottom atom layers locked from movement, simulating the stiffer substrate, and periodic boundary conditions in the plane of the plate are applied.