We propose a finite element model for the dielectric response of nanocomposites of silver nanoparticles, described as polarizable dielectric spheres and ellipsoids, embedded in a dielectric matrix. A methodology for fitting the FEM to a quantum mechanical polarization model is also presented. When fit to a suitable quantum mechanical training set, an ellipsoidal model faithfully reproduces the polarizability of gas phase particles, including the anisotropy due to shape effects. For nanocomposite systems, the FEM requires the use of an accurate definition for the electron delocalization volume, as well as the addition of an interfacial layer to the model. A model containing ellipsoidal inclusions and an interfacial layer of high permittivity was found to reproduce the permittivities of with rod-and disklike inclusions with reasonable fidelity, even though the interfacial permittivity was fitted on a set of nanocomposites with spherical inclusions. The FEM allows the estimation of permittivities for systems that cannot be treated quantum mechanically, such as systems with large anisotropic inclusions, over a large range of inclusion loadings. Furthermore, analysis of the FEM data provides insight into local field effects and the coupling of polarization between components, that is complementary to that obtained from quantum simulations.