<p>This study presents a comprehensive theoretical and numerical investigation into the local field enhancement factor (LFEF) and optical bistability (OB) in ZnTe@Ag core-shell nanostructures embedded within dielectric host matrices. Using the quasi-static approximation, Laplace’s equation was analytically solved for both spherical and cylindrical geometries under appropriate boundary conditions. The Kerr-type nonlinearity of the host medium was incorporated to model third-order nonlinear optical effects. The dielectric response of the silver shell was described using a size-dependent Drude model. Numerical simulations revealed that spherical nanocomposites exhibit significantly stronger field enhancement and lower OB threshold intensities compared to cylindrical counterparts. Additionally, increasing the host dielectric constant or core-shell radius ratio resulted in pronounced shifts in resonance peaks and broadened bistability regions. The LFEF was found to be highly tunable with respect to geometry, size, and material composition, reaching intensities up to three times greater in spherical structures. These findings provide crucial insight into the geometric and dielectric modulation of nonlinear optical behavior, supporting the design of nanostructures for use in optical sensing, memory, and switching devices.</p>