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The metastable beta' phase is often the most effective hardening precipitate in Mg-Gd based alloys. In this paper, the structural, elastic and electronic properties of the recently identified beta'-Mg(7)Gd precipitate in Mg-Gd binary alloys were investigated using first-principles calculations based on density functional theory. The lattice mismatches between the coherent beta'-Mg(7)Gd precipitate and alpha-Mg matrix are discussed and used to rationalize the experimentally observed morphology of the precipitate. The mechanical properties were investigated through analysis of the single-crystal elastic constants and the polycrystalline elastic moduli. It is found that beta'-Mg(7)Gd is brittle in nature. Strong covalent bonding in beta'-Mg(7)Gd, as inferred from its electronic structure, further explains its mechanical properties. Our theoretical results show good agreement with experimental measurements.