Density functional theory (DFT) was used to study mechanical properties of orthorhombic and cubic LiBeH3 and cubic NaBeH3. The band gaps were estimated using different approximations available in the WIEN2k code. The elastic constants of LiBeH3 and NaBeH3 were calculated. Both hydrides were found to be stable mechanically. From elastic constants, the bulk modulus and the linear bulk modulus along crystallographic axes of single crystal were calculated. The calculated values of linear bulk moduli were in good agreement with the reported theoretical values. Young's and Shear moduli, Poisson's ratio and micro-hardness for ideal polycrystalline LiBeH3 and NaBeH3 were also calculated. Both these hydrides can be classified as brittle materials according to obtained results. The values of bulk, shear and Young's moduli obtained in our study were higher than those reported for other popular hydrides for hydrogen storage. Shear and elastic anisotropic factors along with Debye temperature are also discussed using theoretical elastic constants. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.