First-principles hybrid functional calculations have been performed to study the crystal structure, band gap energy, and elastic coefficients of GaAs 1− x Bi x solid solutions. Three different structures in prototype wurtzite and orthorhombic symmetries are considered. Compared to O-16 and O-32 supercells, GaAs 1− x Bi x alloys in W-16 structure are more stable with the lower formation energy for a given Bi concentration. The lattice constants of GaAs 1− x Bi x solid solutions follow the Vegard’s Law regardless of the three different structures. Although the band gap decreases with the increase of Bi concentration, the trends of the band gap energy in the W-16, O-16 and O-32 structures are nearly identical. The calculated elastic coefficients and bulk modulus display a discernible downward bowing and there exists a direct correlation between the elastic stiffness coefficients and strains. These results give a good understanding of the properties of GaAs 1− x Bi x solid solutions.