Electronic doping and screening effects in stacked graphene flakes on Ru and Cu substrates have been observed using scanning tunneling microscopy (STM). The screening affects the apparent STM height of each flake in successive layers reflecting the density of states near the Fermi level and thus the doping level. It is revealed in this way that the strong doping of the first graphene layer on Ru(0001) is attenuated in the second one, and almost eliminated in the third and fourth layers. Similar effect is also observed in graphene flakes on Cu(111). In contrast, the strong doping effect is suppressed immediately by a water layer intercalated between the graphene and Ru.