Rare earth element is one kind of strategic materials. Some rare earth elements have been industrialized. They play major roles in permanent magnetism material, lightening, catalysis and hydrogen storage material. In order to understand the rare earth elements more, it is necessary to study the structures of the valence electrons and atoms of them. The valence electron structures and properties of yttrium, scandium and lanthanum group rare earth elements are studied with the empirical electron theory (EET). Based on the valence electron parameters, the melting points and cohesive energies of these rare earth elements are calculated. The calculations accord with those of the measurements. According to the analyses of EET, the structures and the physical properties of rare earth elements depend on the electron emission or transformation between the lattice-electrons and coherent electrons in outer orbital. It is exhibited that the melting point tends to increase with the lattice electron-covalent electron transformation, however, the valence status of rare earth element affects significantly the electron distribution and property. The covalent electron hoppings occur at divalent europium, ytterbium and samarium, and their melting points are related to the electron transformation covalence-electrons. It is different from the others with trivalent status. The theoretical analysis reveals that the cohesive energy is related to the 4f electrons. The contribution to cohesive energy increases with the number of 4f electrons increasing, which may be due to the shrinking effect of the atomic radius for the lanthanum group. The study implies that the characteriscs of rare earth element are due to the relation between their melt pointing and conhesive energy and electronic structure.