Classical molecular dynamics (MD) simulations were performed to study non-adhesive contact at the atomic scale. Starting from the case of Hertzian contact, it was found that the reduced Young’s modulus E* for shallow indentations scales as a function of, both, the indentation depth and the contact radius. Furthermore, the contact of two representative rough surfaces was investigated: one multi-asperity, Greenwood-Williamson-type (GW-type) rough surface—where asperities were approximated as spherical caps—and a comparable randomly rough one. The results of the MD simulations were in agreement for both representations and showed that the relative projected contact areas Arpc were linear functions of nominal applied pressures, even after the initiation of plastic deformation. When comparing the MD simulation results with the corresponding continuum GW and Persson models, both continuum models were found to overestimate the values of Arpc relative to the MD simulation results.