Mechanical properties of homopolymers containing either solid spheres, rods, or platelets are compared using a three-dimensional lattice spring model, and thus, the effects of filler geometry on the mechanical behavior of the composite are isolated. In addition, the properties of exfoliated and intercalated nanocomposites are examined and the source of the increased reinforcement efficiency in nanocomposites, as a consequence of platelet exfoliation, is elucidated. Viscoelastic deformations are explicitly incorporated in the lattice spring model and, thus, the mechanical response of these filled polymer materials are determined.