The reaction between hydrogen and erbium has been studied by DFT calculations. The enthalpies of formation of the compounds Er, ErH, ErH2 and ErH3 generated by the ordered insertion of hydrogen atoms in the tetrahedral and octahedral (or triangular) sites of the fcc and hcp structures have been calculated. In addition, ErH3 has been calculated with its reported trigonal superstructure. The results of the calculations are consistent with the experimental observation of the sequence Er (hcp) -> ErH2 (fcc) -> ErH3 (trigonal), qualitatively, and with the measured enthalpies of formation, quantitatively. Additionally, the densities of states of all the compounds are studied in detail. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.