We studied single-crystal copper of three different crystallographic orientations [(100), (011) and (111)] for nanoindentation response via a numerical simulation model using spherical indenters of radius (R) 3.4 μm and 10 μm. The model uses rate-independent crystal plasticity with a finite strain implemented as a user routine in the commercial finite element software ABAQUS. The model takes into account active crystallographic slip, orientation effects during nanoindentation computation, and the effect of friction between the indenter and copper substrate. We compared the load–displacement curve and indentation pile-up patterns obtained from the simulations with experimental measurements available in the literature. The indentation load and mean effective pressure beneath the indenter p _m were found to be highest for (111) orientation and lowest for (100). The simulation and experimental data agree well.