Density functional theory calculations are used herein to explore the effect of hydrogen on the electronic, mechanical and phonon properties of LaMgNi4 and its hydrides. The polycrystalline elastic moduli, Poisson's ratios and Debye temperatures are calculated based on the single-crystal elastic constants and Voigt-Reuss-Hill approximations. It is also found that all these materials are metallic behavior, ductile and anisotropic in nature. The mechanical anisotropy is discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The effect of high temperature on the free energy, entropy, and heat capacity are also studied by using the quasi-harmonic Debye model. LaMgNi4 and its hydrides are found to be energetically, mechanically and dynamically stable. Also, they are thermodynamically stable and the order of phase stability is LaMgNi4H7 > LaMgNi4H4 > LaMgNi4H > LaMgNi4. In addition, the highest gravimetric hydrogen storage capacity is found to be 1.74 wt% for LaMgNi4H7. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.