Alloying effects of Zr and Sn on β phase stability and elastic properties in Ti-Nb alloys are investigated within the framework of first-principles density functional theory. Our results suggest that the stability of β phase can be significantly enhanced by the addition of Zr and Sn in Ti-Nb alloys. The computed results indicate that Zr and Sn behave as strong β stabilizers in the Ti-Nb system. The elastic properties are found to be altered considerably by the addition of ternary alloying elements (Zr and Sn). The computed elastic moduli of Ti18.75 at%Nb6.25 at%Zr and Ti25 at%NbxZr compositions are found to be lower than that for Ti18.75 at%Nb6.25 at%Sn and Ti25 at%NbxSn system. The lowest value of ∼54 GPa is obtained for Ti25 at%Nb6.25 at%Zr composition. Furthermore, the directional Young's modulus is found to be in the order of E 100 < E 110 < E 111 for all the compositions of Ti-Nb-Zr and Ti-Nb-Sn system. © 2017 IOP Publishing Ltd.