This paper aims to investigate some fundamental problems of mechanics and physics in the nano-indentation of silicon monocrystals with the aid of molecular dynamics analysis. The study showed that inelastic deformation of silicon monocrystals is solely caused by amorphous phase transformation. Dislocations do not appear and purely elastic deformation exists only in an extremely narrow regime. The onset of inelastic deformation can be predicted by a criterion considering either the octahedral or maximum shear stress. Due to phase transformation, the conatct area between indenter and specimen varies in a very complex manner. The study offers a new theory for the nano-indentation of monocrystalline silicon.