Polymers have various attractive properties (e.g., low volume mass density, low cost and excellent degradation resistance), and hence, they have become essential for a wide range of applications (e.g., aerospace, oil and gas and renewable energy industries). However, due to their limited mechanical, thermal and electrical properties in comparison with typical metallic materials (e.g., steel and aluminum alloys), polymers often need to be modified with different types of fillers to meet the requirements of specific applications. A multitude of filler materials (e.g., nano silver particles, carbon nanotubes, graphene) are available with a wide range of geometries, such as spherical, fiber and platelet shapes. Therefore, developing methods for efficiently characterizing and identifying mechanical and physical properties of filler modified polymers is an important engineering task. The objective of this thesis is to create and validate a numerical modeling framework for predicting mechanical, thermal and electrical properties of particulate polymer composites.