Formation process of Earth's core is studied by numerical simulations of flow field in a self-gravitating fluid sphere. The proto-Earth was assumed to have gravitationally unstable three-layered structure initially consists of the uppermost silicate melt layer, the middle iron layer, and the central undifferentiated silicate-rich protocore. This structure of the heavy iron layer overlying the light protocore leads to Rayleigh-Taylor instability. The numerical simulations supports that the fastest mode of the instability is the translation (l=1 mode in spherical harmonics) of the protocore relative to the iron layers, as pointed out by previous studies. Furthermore, the present calculations shows that the translational mode is followed by growth of a gigantic iron drop and intrusion of the iron drop into the protocore. This late stage process is found to be the controlling process of Earth's core formation. In order to complet the core formation within 109 years required by various geophysical and geochemical constraints, the protocore viscosity &eegr;1 should be less than 1026 Pa s, which is larger than the present mantle viscosity but much smaller than the viscosity estimated for the protocore under low temperature and high pressure. Heating of the protocore by gravitational energy released during the core formation, change of flow mechanisms from diffusional flow to either power law creep or plastic flow and effect of volatiles contained in the protocore on the effective viscosity may assist accleration of the core formation process. ¿American Geophysical Union 1993