In this work, we present a detailed study of Al- and Si-doped alpha-, gamma-, and beta-MgH2 phases using the gradient corrected density functional GGA-PBE and the hybrid Hartree-Fock density functionals PBE0 and HSE06 within the framework of generalized Kohn-Sham density functional theory (DFT) using a plane-wave basis set. We investigate the structural, electronic, and thermodynamical properties of these compounds with regard to their hydrogen storage effectiveness. PBE0 and HSE06 predict cell parameters and bond lengths that are in good agreement with the GGA-PBE calculations and previously known experimental results. As expected smaller band gaps (E(g)s) are predicted by GGA-PBE for the pure magnesium hydride phases. PBE0 overcomes the deficiencies of DFT in treating these materials better than HSE06 and yields E(g)s that compare even better with previous GW calculations. Both the hybrid functionals increase the E(g)s of the Al-doped magnesium hydrides by much less magnitudes than of the Si-doped phases. This difference is interpreted in terms of charge density distributions. Best H-2 adsorption energies (Delta H-ads) are computed by HSE06 while GGA-PBE significantly overestimates them. Si-doped alpha- and beta-MgH2 exhibited the least negative Delta H-ads in close proximity to the H-2 binding energy range of -0.21 to -0.41 eV ideal for practical H-2 storage transportation applications. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.