Composition dependence of Young's modulus in β Ti-V and Ti-Nb binary alloys and Sn-added ternary alloys quenched from β phase region was investigated at room temperature in relation to the stability of β phase. A minimum of Young's modulus in the binary alloys appears at such a composition that athermal ω phase transformation is almost completely suppressed. Formation of isothermal ω phase by aging after quenching increases Young's modulus. Sn addition to the binary alloys suppresses or retards ω transformation, thereby decreasing Young's modulus. Optimization of alloy composition in Ti-Nb-Sn alloys leads to low Young's modulus of about 40 GPa. The composition dependence of Young's modulus obtained experimentally in this study can be qualitatively explained by the theoretical discrete-variational Xα cluster method.