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The orientation, hardness and Young's modulus of Al3Yb single crystal were analyzed using the electron back scatter diffraction (EBSD) and nanoindentation techniques, combined with the first principles calculations. The Al3Yb single crystal of about 1 mm size could be obtained by heating hypereutectic Al-38.5 (wt%)Yb alloy to liquid state and cooling to room temperature at 60 °C/h. The results showed that the hardnesses of the Al3Yb single crystals oriented in (318), (023), (213), (112) and (122) directions varied between 5.4 ± 0.1 and 5.7 ± 0.1 GPa, and the reduced modulus were between 131.9 ± 1.6 and 140.5 ± 3.9 GPa. First principles calculations by assuming standard Yb pseudopotential with 4f electrons showed that the elastic constants of C11, C12 and C44 were 149.4, 32.94 and 66.59 GPa, respectively, and the Poisson's ratio was 0.161. Based on these calculated elastic constants and Poisson's ratio and the reduced modulus values, the Young's modulus of the Al3Yb single crystal was determined to be between 148.4 ± 2.3 and 154.9 ± 2.3 GPa for different orientations and the anisotropy coefficient (A) was 1.17 ± 0.01.