<p>To search for excellent Re-Zr ultrahigh-temperature alloys, the first-principles method has been used to study the structural, mechanical, and thermodynamic properties of five Re-Zr alloys. The results show that two novel cubic phases, ReZr and Re₃Zr, are predicted first. The convex hull indicates that Re₂Zr has better thermodynamic stability compared to the other Re-Zr alloys. It has been found that the elastic modulus of Re-Zr alloys increases with increasing Re concentration. In particular, these Re-Zr alloys show better ductility with a high elastic modulus. Naturally, the high elastic modulus is that the high-concentration Re enhances the localized hybridization between Re and Zr atoms, and between Re and Re atoms. Furthermore, the elastic modulus of Re₂₄Zr₅ is higher than that of the other four Re-Zr alloys. The high elastic modulus of Re₂₄Zr₅ is related to its octagonal Re-Re cage structure, which is composed of four Re-Re bonds. Finally, it has been found that the thermodynamic properties of Re₂₄Zr₅ are better than that of the other Re-Zr alloys.</p>