Recent developments showed that β-type Ti-Nb alloys are good candidates for hard tissue replacement and repair. However, their elastic moduli are still to be further reduced to match the Young's modulus values of human bone, in order to avoid stress shielding. In the present study, the effect of indium (In) additions on the structural characteristics and elastic modulus of Ti-40 Nb was investigated by experimental and theoretical (ab initio) methods. Several β−type (Ti-40 Nb)-xIn alloys (with x≤5.2 wt.-%) were produced by cold-crucible casting and subsequent heat treatments (solid solutioning in the β-field followed by water quenching). All studied alloys completely retain the β-phase in the quenched condition. Room temperature mechanical tests revealed ultimate compressive strengths exceeding 770 MPa, large plastic strains (> 20%) and a remarkable strain hardening. The addition of up to 5.2 wt.-% indium leads to a noticeable decrease of the elastic modulus from 69 GPa to 49 GPa, which is closer to that of cortical bone (< 30 GPa). The Young's modulus is closely related to the bcc lattice stability and bonding characteristics. The presence of In atoms softens the parent bcc crystal lattice, as reflected by a lower elastic modulus and reduced yield strength. Ab initio and XRD data agree that upon In substitution the bcc unit cell volume increases almost linearly. The bonding characteristics of In were studied in detail, focusing on the energies that were appearing from the EDOSs significant for possible hybridizations. It came out that minor In additions introduces low energy states with s character that present antibonding features with the Ti first neighbouring atoms as well as with the Ti-Nb second neighboring atoms thus weakening the chemical bonds and leading to elastic softening. These results could be of use in the design of low rigidity β-type Ti-alloys with non-toxic additions, suitable for orthopedic applications.