Density functional theory calculations within the generalized-gradient approximation are used to establish the ground-state structure, equilibrium structural parameters, and electronic structure for MBeH3 phases. From the 24 structural arrangements used as inputs for structural optimization calculations, the ground-state crystal structures of MBeH3 phases have been predicted. At ambient conditions, LiBeH3 and NaBeH3 Crystallize with perovskite-related orthorhombic and cubic structures, respectively. The remaining phases KBeH3, RbBeH3, and CsBeH3 crystalize in a monoclinic structure. In the predicted phases one can store up to 15.93 wt % of hydrogen. The formation energy for the MBeH3 phases have been investigated along different reaction pathways. The electronic structures reveal that all these phases are insulators with estimated band gaps varying between 1.79 and 3.44 eV.