We provide an analytical solution for studying the near-field optical effect of a core-shell nanostructure in proximity to a flat surface, within quasi-static approximation. The distribution of electrostatic potential and the field enhancement in this complex geometry are obtained by solving a set of linear equations. This analytical result can be applied to a wide range of systems associated with near-field optics and surface plasmon polaritons. To illustrate the power of this technique, we study the field-attenuation effect of an oxidized shell in a silver tip in a near-field scanning microscope. The thickness of oxidized layer can be monitored by measuring the intensity of light. We also find a linear relation between resonant frequency and temperature in an Ag-Au core-shell structure, which provides insight for local temperature detection with nm scale resolution. Our results also show good agreement with recent finite element method results.