The scope of this work is the study of hydrogen atom interaction with the graphite surface taken as a model of the interactions that occur in the tokamaks (magnetic confinement fusion devices) between the carbon covered wall and the hydrogen ions (H+ or D+ or T+) coming out of the plasma. This study is performed at the atomic scale in the framework of the density functional theory. The graphite surface is modeled by the (0001) layer in either a periodic or a molecular approach. The clusters best reproducing the periodic two-dimensional results were selected to investigate hydrogen-graphite interaction. One- and two-layer clusters were used to model the basal plane and the bulk of graphite. It was found that hydrogen atoms could be bonded to the surface and in the bulk with an exothermic energy. The potential-energy barriers corresponding to the over crossing of the first surface layer by an atomic hydrogen have been determined. The H+H recombination (Eley-Rideal mechanism) was investigated on the surface and in the bulk. The quantitative results concerning the ability of hydrogen atoms to penetrate into the bulk through the basal plane of graphite is linked to the hydrogen uptake at the walls of the tokamak during the plasma discharges.