A generic finite-element based approach for predicting the behavior and properties of multiphase materials comprised of anisotropic, arbitrarily shaped and oriented phases is presented. The approach is exact in principle and effective in practice. It is the consistent use of periodic boundary conditions in the course of generating multiinclusion Monte Carlo configurations, dividing them into morphology-adaptive quality meshes, and numerical solution for the overall, effective propel-ties that extracts an accurate prediction of the behavior and properties of multiphase materials from remarkably small computer models. The approach is employed to identify numerically the technological potential of some whisker- and platelet-filled polymers. It is demonstrated that the filled polymers studied have an appealing, currently unrealized technological potential. This potential has essentially been overlooked because of the widespread use of empirical equations tuned to reproduce available experimental data that unavoidably reflect the existing technological level.