In present work an atomic hydrogen interaction with RG-Ti graphite and two types of pyrolytic graphite was studied using thermal desorption experiments. Contrary to molecular hydrogen interaction atomic hydrogen sorption by all investigated graphite types has similar features. Sorption of atoms grows rapidly for small fluences and has saturation at a level about 10(15) H-2/cm(2) for fluences above 10(17) H-0/cm(2) On thermal desorption spectra two maximums were observed which may be related to hydrogen detrapping from traps with different binding energies. However some observed peculiarities in desorption process could not be described by detrapping only. Mathematical model has been proposed to describe these features. Rate constants of different elementary processes have been determined.