BaScO3 and its hydride BaScO3H0.5 have been investigated using density functional theory (DFT) with the generalized gradient approximation (GGA). BaScO3 perovskite can crystallize in five possible crystal structures: orthorhombic (Pnma), tetragonal (P4mm), rhombohedral (R-3c), hexagonal (P63/mmc), and cubic (Pm-3m). These five possible phases have been optimized to obtain the most stable phase of BaScO3. The orthorhombic phase, being the most stable and having the lowest volume among the studied phases, has been considered for hydrogen bonding studies, and BaScO3H0.5 has been obtained. The electronic properties including band structure and corresponding partial density of states have been obtained for both BaScO3 and BaScO3H0.5 compounds. In addition, partial charge analysis has been performed. The calculated elastic constants have been used to obtain mechanical properties, such as bulk modulus, shear modulus, Young's modulus, and Poisson's ratio. Also, direction-dependent elastic properties have been studied in two dimensions and three dimensions. BaScO3 and BaScO3H0.5 compounds have ionic bonding and they are ductile materials. Moreover, the hydrogen storage properties of BaScO3H0.5 have been investigated and it is found that the gravimetric hydrogen storage capacity is 0.22 wt% and the hydrogen desorption temperature is determined as 1769.70 K.