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Based on a certain ratio of Zr and Ti atomic fractions according to Zr₄₇Ti₄₅Al₅V₃ (wt.%), the lattice constants, lattice stability, and elastic properties of Zr-Ti-X alloys (X = Al, V) in body-centered cubic (BCC) (β phase) and hexagonal close-packed (HCP) (α phase) crystal structures were studied using first-principles calculations. It is shown that Al acts as an α stabilizer for Zr-Ti-Al alloys and V can stabilize the β phase for Zr-Ti-V alloys. As the mass fraction of Al increases from 4 wt.% (Zr₅₅Ti₄₁Al₄) to 6.8 wt.% (Zr_53.2Ti₄₀Al_6.8), these alloys all have relatively good strength, hardness, and rigidity, however, their ductility deteriorated with the increasing of Al mass fraction. When the mass fraction of V in Zr-Ti-V alloys is 2.4 wt.%, Zr_55.6Ti₄₂V_2.4 (wt.%) achieved the best strength, hardness, and rigidity, when the mass fraction of V increases from 0 (Zr₅₇Ti₄₃) to 12 wt.% (Zr_50.2Ti_37.8V₁₂), their ductility improved. The changes of phase compositions and structure with Al content or V content distinctly affect mechanical properties of ternary Zr-Ti-X alloys (X = Al, V), the amount of Zr and Ti could be factors that impact the mechanical properties of the multiphase Zr₄₇Ti₄₅Al₅V₃ from the point of view of ternary Zr-Ti-Al and Zr-Ti-V compositions.