First-principles calculation reveals that the Ti100-xAlx-H phases with hydrogen at octahedral(O) interstitial sites are energetically more favorable than corresponding tetrahedral(T) interstitial sites, and that the O and T sites become thermodynamically stable with negative heats of formation when x is less than about 57 and 38, respectively. Calculation also shows that H has an important effect on mechanical properties of TiAl-H phases, and that the TiAl-H phases with H at O sites are more brittle with bigger elastic moduli than corresponding T sites. In addition, three anisotropic indexes are used to express the elastic anisotropy of various TiAl and TiAl-H phases, and the changes of elastic anisotropy are discussed in terms of electronic structures. The calculated results are compared with available experimental results in the literature and the agreements between them are fairly good. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.