The mechanical properties and the deformation mechanism of Cu single crystal metal and bi-crystal Cu metals are explored by the molecular statics simulations for the nanoindentation and nanoscratching process. In the simulation of nanoindentation, the relationship of load, influenced depth and displacement are obtained to investigate the deformation mechanism of Cu metals. The variations of averaged bond length are used to understand condition of atoms deformation. For the nanoindentation on two single crystal surfaces, our results indicate that the influenced depths can be affected by the tip indentation and the motion of dislocations. In the case of the bi-crystal system, because the interfaces between two crystal orientations can provide the resistance to the motions of dislocation, the influenced depths can be affected by the existence of the interface. Eventually, the variations of averaged bond length are also used to explore the structural deformation under the different nanoindentation depths and nanoscratching distances during the nanoscratching process. Moreover, the deformation mechanism during nanoindentation and nanoscratching process are also discussed in this article.