Titanium alloys are favorable implant materials for medical applications, due to their desirable mechanical properties and biochemical compatibility. However, current bio-titanium alloys were formulated principally by trial and error, which by no means represents the optimum. Here a theoretical investigation of the influence of alloying elements and interstitial elements on the bulk modulus and theoretical strength of α-titanium was presented. The bulk modulus and theoretical strength were estimated from the binding energy against the unit cell volume curves calculated by means of first principles discrete variational cluster method. The results of the calculation suggested that the 3d elements Cr, Mn, Fe, and Co, as well as all the interstitial elements considered in this study (H, B, C, N and O), are capable of enhancing the relative admissible strain of α-titanium.