Herein, first principles computer-based simulations were performed to predict the ground-state structure, mechanical stability, and magneto-electronic properties of BaMO₃ (M = Mg and Ca) perovskites, which have not been experimentally synthesized to date. Structural optimization authenticate the stability in the cubic structure for BaMO₃ perovskites having symmetry of the Pm3m space group. The tolerance factor and cohesive energy further validate the stability of BaMO₃ in the cubic phase. Moreover, mechanical stability was confirmed by the positive elastic constants, satisfying the necessary stability conditions. The band structure and density of states at the optimized lattice constants revealed the ferromagnetic half-metallic character of BaMO₃ materials, with O–p states playing a prominent role. The half-metallic character originates from the partial filling of the O–p states in the spin-down channel. Spatial charge distribution indicated the dominant ionic character of bonding. No change in the magnetic moment of perovskites was observed upon changing the M-site atoms. Various elastic parameters suggested that these perovskites are ductile in nature with highly anisotropic character. The three-dimensional graphical representation of different elastic moduli revealed that the linear compressibility is isotropic, whereas the shear modulus, Young's modulus, and Poisson's ratio of these perovskites are highly anisotropic. The results obtained in this study are in agreement with those reported in the literature for other similar perovskites.