  The charge distribution induced by external fields in finite stacks of
graphene planes, or in semiinfinite graphite is considered. The interlayer
electronic hybridization is described by a nearest neighbor hopping term, and
the charge induced by the self consistent electrostatic potential is calculated
within linear response (RPA). The screening properties are determined by
contributions from inter- and intraband electronic transitions. In neutral
systems, only interband transitions contribute to the charge polarizability,
leading to insulating-like screening properties, and to oscillations in the
induced charge, with a period equal to the interlayer spacing. In doped
systems, we find a screening length equivalent to 2-3 graphene layers,
superimposed to significant charge oscillations.
