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　degrees　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　C-11,　C-12　and　C-44　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.