The formation and evolution of the solid electrolyte interface (SEI) film during the first electrochemical intercalation of lithium into graphite were modeled as a special precipitation process including a nucleation phase of the SEI film's solid deposition, and followed by a growth phase involving the precipitation of new solids on previously formed solid nuclei. It was shown that the solid species can nucleate in the electrolyte solution, directly on the graphite surface, or adjacent to an already present particle on the graphite surface when precipitating from the electrolyte solution. Within the framework of classical nucleation theory (CNT), we can qualitatively explain the origin of the two-layer structure of SEI films, which consists of a thin, compact polycrystalline or heteromicrophase layer rich in inorganic species (e.g., LiF, Li2O) close to the electrode, and a thicker porous and amorphous layer composed mainly of organic compounds (e.g., ROLi, ROCO2Li) that is farther from the graphite.