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The anisotropic mechanical properties of crystal surface of single crystal germanium, (100), (110) and (111) were studied, through nano indentation experiments. According to the load displacement curves of nano indentation processes and the theory of Oliver-Pharr, the elastic modulus and the hardness of the materials were investigated. The experimental results show that obvious plastic deformation occurred in single crystal germanium in the process of nano indentation and the plasticity of Ge（110）is the best, Ge（100）is worse than Ge（111), and the Ge（111）is the worst. And the hardness and the elastic modulus have similar change trend. When the indentation depth is shallow, significant fluctuations appeared on the hardness and the elastic modulus, affected by the surface effect. And because the atomic density of each crystal surface and the interplanar spacings are quite different, single-crystal germanium exhibits stable anisotropy, and the hardness and the elastic modulus rank from high to low as follows: (111) crystal plane, (110) crystal plane, (100) crystal plane. As the indentation depth increases, the hardness and the elastic modulus gradually stabilize, and the order from high to low are (110) crystal plane, (100) crystal plane, (111) crystal plane.