The aim of this paper is to investigate the structural, electronic, optical and elastic properties of the cubic AlxGa1-xSb ternary alloy with their related binary compounds GaSb and AlSb. The calculations are performed within density functional theory (DFT) using full-potential linearized augmented plane wave (FP-LAPW) method as implemented in Wien2k package. It is found that the lattice parameter of the AlxGa1-xSb ternary alloy shown a non-linear variation with the Aluminum (Al) mole fraction. Beside, the band gap variations with the composition of the ternary alloy exhibit also a small deviation from the Vegard's law, and the obtained results confirm the semiconducting character of the studied materials. Furthermore, the optical properties of the materials are calculated and compared with the theoretical models and with the experimental data found in the literature where a good agreement is observed. The elastic properties of the studied alloys are also determined in this study and they are compared with other works available in the literature.