This study investigates the structural, elastic, optical, and electronic properties of Ba₂MBiO₆ (M = Sm, Tb) oxide double perovskites using Density Functional Theory (DFT) with the Wien2k code. The generalized gradient approximation (GGA) is used for structural and elastic properties, while the Tran-Blaha modified Becke-Johnson (TB-mBJ) functional is used for optical and electronic properties. The structural stability of both compounds is verified using the Birch-Murnaghan equations of state and tolerance factors. Both systems are found to be elastically stable with anisotropic ductile and ionic bonding behavior. Ba₂SmBiO₆ is a non-central force crystal (v = 0.51), while Ba₂TbBiO₆ is a central force crystal (v = 0.29). Ba₂SmBiO₆ exhibits half-metallic behavior with spin-dependent band gaps, making it a potential candidate for spintronic applications. Ba₂TbBiO₆ behaves as a direct band gap semiconductor with a band gap of 1.79 eV. Both compounds have optical properties in the UV-visible region, indicating potential for optoelectronic applications. Perovskite oxides are promising materials for various applications due to their structural and compositional flexibility. However, their use in spintronics and energy applications is limited by structural instability, thermodynamic problems, and low Curie temperatures. This study aims to explore the potential of Ba₂MBiO₆ (M = Sm, Tb) for mechanical and spintronic applications, providing reference data for experimental investigations. The computational methodology involves DFT calculations using the FPLAPW+lo scheme, GGA-PBE for exchange-correlation interactions, and TB-mBJ for optoelectronic properties. The results show that Ba₂MBiO₆ has promising properties for spintronic and optoelectronic applications.This study investigates the structural, elastic, optical, and electronic properties of Ba₂MBiO₆ (M = Sm, Tb) oxide double perovskites using Density Functional Theory (DFT) with the Wien2k code. The generalized gradient approximation (GGA) is used for structural and elastic properties, while the Tran-Blaha modified Becke-Johnson (TB-mBJ) functional is used for optical and electronic properties. The structural stability of both compounds is verified using the Birch-Murnaghan equations of state and tolerance factors. Both systems are found to be elastically stable with anisotropic ductile and ionic bonding behavior. Ba₂SmBiO₆ is a non-central force crystal (v = 0.51), while Ba₂TbBiO₆ is a central force crystal (v = 0.29). Ba₂SmBiO₆ exhibits half-metallic behavior with spin-dependent band gaps, making it a potential candidate for spintronic applications. Ba₂TbBiO₆ behaves as a direct band gap semiconductor with a band gap of 1.79 eV. Both compounds have optical properties in the UV-visible region, indicating potential for optoelectronic applications. Perovskite oxides are promising materials for various applications due to their structural and compositional flexibility. However, their use in spintronics and energy applications is limited by structural instability, thermodynamic problems, and low Curie temperatures. This study aims to explore the potential of Ba₂MBiO₆ (M = Sm, Tb) for mechanical and spintronic applications, providing reference data for experimental investigations. The computational methodology involves DFT calculations using the FPLAPW+lo scheme, GGA-PBE for exchange-correlation interactions, and TB-mBJ for optoelectronic properties. The results show that Ba₂MBiO₆ has promising properties for spintronic and optoelectronic applications.