First principles calculation reveals that the TiAlH phases become relatively less stable after the addition of more H atoms, and that the H migration from tetrahedral interstitial site to octahedral site in gamma TiAl should be much easier than that between octahedral sites. Calculation also shows that H concentration has an important effect on mechanical properties of TiAlH phases, and that the energetically favorable TiAlH phase should possess bigger E, G, and G/B values as well as lower elastic anisotropy. Moreover, it is found that the heat capacities of TiAlH phases increase with the increase of H concentration, and that the coefficients of thermal expansion of TiAl and TiAlH phases decrease with the increase of pressure.,Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.