Superior electrical, thermal, and mechanical properties of carbon nanotubes have made them popular candidates for use as fillers in polymer nanocomposites. This thesis presents a numerical model developed to determine the electrical and heat transport properties of these materials via percolation theory. Realistic nanocomposite representative volume elements are generated in three-dimensional space according to user-defined input parameters. A spanning network algorithm is used to search for connections between nanotubes. Interconnected nanotubes are then converted into equivalent resistor networks. The resistor network is then examined using finite element analysis through Kirchoff’s current law for electrical transport, and Fourier’s law for thermal transport. Monte Carlo simulations eliminate statistical variation at each volume fraction of nanotube filler. Several boundary treatment methods are examined to determine which is the most computationally efficient. The model is validated through comparison to experimental data reported in the literature. The presented model is unique in that it can predict both the electrical and thermal conductivity of carbon nanotube based polymer nanocomposites.