Using ab initio alloy theory, we systemically investigate the effect of alloying elements on the elastic properties of body-centered cubic (bcc) Ti1−x−yMoxMy (0.05 ≤ x ≤ 0.2; 0 ≤ y ≤ 0.4; M = Mg, Mn, Ni, Zr, Nb, and W) alloys. The theoretical single-crystal and polycrystalline elastic moduli of Ti1−xMox (0.05 ≤ x ≤ 0.2) agree well with the available experimental values and previous theoretical data. The lattice parameters of Ti-Mo-M ternary alloys significantly increase (decrease) with increasing Mg and Zr (Mn and Ni) contents, while remain almost constant for Nb and W additions. It is found that Mg is a promising alloying element that could decrease the Young’s modulus of bcc Ti-Mo alloys, but its content should be as small as possible since the stability of the β phase decreases with increasing Mg concentration. On the other hand, Mn, Ni, Nb, Zr, and W enhance the Young’s modulus and the stability of the β phase.