The results of calculations of the elastic properties of quenched biocompatible titanium based Ti–26% Nb, Ti–26% Nb–3% Zr, Ti–26% Nb–6% Zr, Ti–26% Nb–3% Zr–1%Sn, and Ti–26% Nb–3% Zr–1% Sn–0.7Ta alloys (in at %) are presented and compared with the literature and experimental data on estimating the elasticity modulus of alloys by microindentation. Microstructural and X-ray diffraction analysis showed that the studied alloys subjected to quenching from the β-region contain a single-phase metastable solid β-solution prone to twinning under cold deformation as follows from the location of the alloys in the Bo‒Md diagram. Good agreement has been established between the calculated and experimental values of the elastic properties, as characterized by an increase in the shear and Young moduli and a decrease in the Poisson coefficient with an increase in the molybdenum equivalent, which determines the stability of a solid alloy β‑solution.