Mechanical properties of NaMgH3 were investigated using the norm-conserving pseudopotentials and plane waves (PP-PW) within the general gradient approximation (GGA) in the frame of density functional theory (DFT). The elastic constants of NaMgH3 were calculated for the first time. The NaMgH3 compound is found to be mechanically stable at ambient pressure. The linear bulk modulus and the bulk modulus along crystallographic axes of single crystals have been derived using elastic constants. The calculated linear bulk moduli are found to be in good agreement with the theoretical value reported in the literature. Shear and Young's moduli as well as Poisson's ratio for ideal polycrystalline NaMgH3 are also calculated. According to the obtained results, NaMgH3 can be classified as brittle material. The shear anisotropic factors and the elastic anisotropy are also discussed. A Debye temperature of 648 K was also determined using theoretical elastic constants. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.