Molecular dynamics simulations are used to demonstrate for the first time that systems about 4 nm thick containing 1200-1600 water molecules and NaCl at 1-3M concentrations exhibit the main components of electric double layers at charged metal surfaces. In particular, for the system chosen, there are regions clearly identifiable as a bulk electrolyte zone, a diffuse layer that screens the charge on the electrode, and a layer of oriented water localized next to the electrode. The width of the diffuse layer increases with decrease in salt concentration from 0.2 nm at 3M to 0.5 nm at 1M. All the calculations are based on the simple point-charge (SPCE) water model and the immersed-electrode approximation.