We investigate the intercalation of hydrogen at the graphene/SiC(0001) interface through atomistic models characterized by very low strains both in the epitaxial graphene and in the SiC substrate. Adsorption of H at the interface is always stable but shows energy variations larger than 1 eV between different locations of the interface. An interface model presenting a strong interaction of graphene with the substrate, corresponding to the experimental situation, shows that adsorption at the interface is on average 0.75eV less stable than at the surface of the buffer layer. At variance, a model having a much weaker graphene/SiC interaction results in hydrogenation energies that are comparable in the two cases. The structural modifications occurring upon H intercalation show a partial conversion of the buffer layer into quasi-free standing graphene, accompanied by a marked downward relaxation of the hydrogenated Si atom and a local steric repulsion between the latter and the overlying graphene. (C) 2013 Elsevier B.V. All rights reserved.