Abstract <p>The elastic properties of a number of binary titanium alloys Ti–Me (Me = V, Nb, Mo, Ta) with a body-centered structure were calculated using the exact muffin-tin orbital method in the coherent potential approximation. It is shown that the elastic constants <i>C</i>₁₁ and <i>C</i>₁₂ increase with concentration of the second component in β-Ti–Me alloys, although the latter weakly depends on the concentration. However, <i>C</i>₄₄ decreases in the presence of V and Nb and increases in the presence of Mo and Ta. According to the calculated densities of electronic states, the concentration behavior of <i>C</i>₁₁ is due to an increase in chemical bonding with the second neighbors, which is most pronounced with an increase in the number of <i>d</i> electrons of the alloying element. It is found that all the studied binary alloys have the lowest Young’s moduli near the β-phase instability region and in the ‹100› direction. With growing tantalum concentration, the anisotropy of Young’s modulus decreases, but its pattern remains unchanged. However, V-, Nb- and Mo-containing alloys become practically isotropic at a certain concentration of the second component, and their anisotropy pattern changes. In general, the obtained elastic characteristics of binary titanium alloys are in good agreement with the available experimental and theoretical data.</p>