We herein investigate the interaction of beryllium with a graphene sheet and in a bilayer of graphite by means of periodic DFT calculations. In all cases, we find the beryllium atoms to be more weakly bonded on graphene than in the bilayer. Be(2) forms both magnetic and non-magnetic structures on graphene depending on the geometrical configuration of adsorption. We find that the stability of the Be/bilayer system increases with the size of the beryllium clusters inserted into the bilayer of graphite. We also find a charge transfer from beryllium to the graphite layers. All these results are analysed in terms of electronic structure.