The nano-indentation test for 6H-SiC is carried out with a Berkovich indenter. The indentation surface morphology is analyzed by SEM, which show that when the maximum load Pmax is 8 mN, there is only plastic deformation and no cracks on the surface of workpiece after unloading process, and when Pmax is 10 mN, there is the initiation of crack occurring on the surface of workpiece after unloading process. Based on the strain hardening model, the three-dimensional finite element method of nano-indentation for 6H-SiC is carried out. Simulation results show that in the unloading process the maximum stress and the maximum strain occur in the contact area between the workpiece with the indenter edges, which is consistent with the experimental results. When propagate to the surface from the subsurface, the cracks are subjected to the type I stress and the type II stress due to elastic recovery. After propagating to surface of workpiece, the cracks propagate along a fixed direction because the proportion of type I stress is much larger than that of type II stress. The influence of the cleavage plane on the propagation direction of cracks is obvious. The cracks propagate more easily when the indenter edges are along cleavage plane. The indentation depth and residual depth increase with the increase of Pmax. While, the elastic recovery rate gradually decreases and tends to be stable with the increase of Pmax. When Pmax is <10 mN, the micro-hardness and the elastic modulus increase linearly with the increase of Pmax. When Pmax exceeds 10 mN, the micro-hardness decreases with the increase of Pmax and then gradually tends to be stable, and the elastic modulus increases by power function with the increase of Pmax and then gradually tends to be stable.