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Structural stability, sound velocities, elasticity, and thermodynamic properties of cubic Zr_0.5Nb_0.5 alloy have been investigated at high pressure and high temperature by first-principles density functional calculations combined with the quasi-harmonic Debye model. A pronounced pressure-induced shear wave velocity stiffening in Zr_0.5Nb_0.5 alloy is observed at pressures above ~11 GPa, owing to its structural instability under high pressure, whose anomalous behavior is also observed in the end members of Zr-Nb alloys for Zr at ~13 GPa and for Nb at ~6 GPa upon compression, respectively. In addition, high-pressure elasticity and elastic-correlated properties of cubic Zr_0.5Nb_0.5 are reported, as compared with previous studies on Zr-Nb alloys with different compositions. A comprehensive study of the thermodynamic properties of cubic Zr_0.5Nb_0.5, such as heat capacity (<i>C_v</i>), thermal expansion coefficients (<i>α</i>), and Debye temperature (<i>Θ_D</i>), are also predicted at pressures and temperatures up to 30 GPa and 1500 K using the quasi-harmonic Debye model.