The energetics of single and multiple H atoms inside Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12 and YAlO3 as well as the migration behavior of H atom have been investigated using first-principles calculations. Among these oxide matrixes, single H atom inside Y2TiO5 is most energetically stable, followed by Y2O3, Y2Ti2O7, Y3Al5O12 and YAlO3. The migration barrier of H atom in Y2O3 is lower than that in other oxide crystals. The formation energy and migration barrier of H atom in those oxide crystals are always higher than that in alpha-Fe. He atom is more stable than H atom inside oxide crystals, contrarily to the trend in alpha-Fe solid. Generally, in the cases of Fin (1 <= n <= 4) atoms inside oxide crystals, the formation energy of even-sized H-n cluster is lower than that of odd-sized H-n clusters, because two H atoms form a hydrogen molecule with strong H-H covalent bond. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.