In the present study, the Density Functional Theory (DFT) implemented in Vienna Ab-initio Simulation Package(VASP) code was employed to investigate the β phase stability and elastic properties of Ti-xMo-Sn (x=1-5) alloys. The structural properties were investigated after geometrical optimization. The general elastic properties (such as bulk modulus B, shear modulus G, Young"s modulus E) were estimated by Voigt-Reuss-Hill approximation. In addition, the valence electron criterion for design of low Young"s modulus Ti-xMo-Sn alloys was proposed. The calculated cohesive energy indicate that Mo can increase the β phase stability of Ti-xMo-Sn alloys. The Pugh ratio B/G and Poisson"s ratio ν suggest that all these alloys exhibit ductile properties. For Ti-xMo-Sn alloys, the smaller tetragonal shear constant C′ may induce the lower Young’s modulus. Ti-3Mo-Sn possess the lowest Young’s modulus (48.47 GPa) and best ductility, showing great potential for biomedical applications. The elastic anisotropy A of Ti-xMo-Sn alloys is sensitive to Mo concentration, the lowest Young’s modulus always oriented in the <100> crystallographic direction. In the end, detailed analysis of total and partial DOS explained the calculated results.