A general formulation of the collective oscillation of electrons in solids are developed to take into account fully effects of ion-core potential. Based on the second quantized scheme of the many-body system, the collective component of density fluctuation is examined carefully and it is shown that we can define a set of the collective normal co-ordinates under the specified conditions. In Section 3, the many-electron Hamiltonian is transformed into the Hamiltonian of the collective field and of the electrons with a modified electron-electron interaction and the interaction Hamiltonian between the collective field and the electrons. In Section 4, we derive the formula of the generalized “plasma” frequency and that of the dispersion relation.