High alloyed β-phase stabilized titanium alloys are known to provide comparable Young's modulus as that to the human bones (∼ 30 GPa) but is marred by its high density. In the present study the low titanium alloyed compositions of binary Ti-Nb and ternary Ti-Nb-Zr alloy systems, having stable β-phase with low Young's modulus are identified using first principles density functional framework. The theoretical results suggest that the addition of Nb in Ti and Zr in Ti-Nb increases the stability of the β-phase. The β-phase in binary Ti-Nb alloys is found to be fully stabilized from 22 at.% of Nb onwards. The calculated Young's moduli of binary β-Ti-Nb alloy system are found to be lower than that of pure titanium (116 GPa). For Ti-25(at.%)Nb composition the calculated Young's modulus comes out to be ∼ 80 GPa. In ternary Ti-Nb-Zr alloy system, the Young's modulus of Ti-25(at.%)Nb-6.25(at.%)Zr composition is calculated to be ∼ 50 GPa. Furthermore, the directional Young's moduli of these two selected binary (Ti-25(at.%)Nb) and ternary alloy (Ti-25(at.%)Nb-6.25(at.%)Zr) compositions are found to be nearly isotropic in all crystallographic directions. © 2015 Elsevier B.V. All rights reserved.