Abstract: Based on the density functional theory, the Perdew-Burke-Ernzerhof exchange-correlation potential was used to optimize the geometry of double perovskite Sr₂ReNbO₆(Re = La, Gd, Lu) crystals, the stable structures with lowest energy were obtained. Using the optimized structure as a model, density of states (DOS), optical properties contain complex dielectric constant ε(ω), refractive index n(ω), reflectivity R(ω) and distinction coefficient k(ω) were calculated receptivity, and the influence of incident photon energy on the optical properties of the materials were analyzed. The elastic constants C_ij of Sr₂ReNbO₆(Re = La, Gd, Lu) crystals were also calculated, according to the C_ij, the mechanical properties include Young’s modulus (Y), bulk modulus (B), shear modulus (G) and Poisson’s ratio (χ) were obtained, and the influence of crystal structure on the mechanical properties of materials were investigated. The results show that the lattice constants of optimized double perovskite crystal structure are in agreement with the available experimental results. The band structure of Sr₂ReNbO₆(Re=La, Gd, Lu) series materials exhibits the semiconducting characteristics, and the cubic Sr₂LaNbO₆ exhibits a direct band structure with band gap of 3.12 eV, whereas the monoclinic Sr₂GdNbO₆ and Sr₂LuNbO₆ exhibit indirect band structure with wider band gap of 3.25 eV and 3.29 eV respectively. The maximum of reflectivity R(ω) of Sr₂ReNbO₆(Re = La, Gd, Lu) are 32.8%, 29.3%, 33% respectively, and these materials own relatively large absorption α(ω). The Poisson’s ratio (χ) of Sr₂ReNbO₆(Re=La, Gd, Lu) crystals are 0.27, 0.28, 0.27 respectively, which indicates that the atoms in these materials are probe to combinate in ionic bond and the nature ductility of these materials.