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A three-dimensional modeling approach is developed to simulate the electrical percolation thresholds in carbon nanotube-based composites, wherein the effects of intertube Van der Waals interactions and electrical tunneling are taken into consideration. Numerical studies using the Monte Carlo method show that these two factors play significant roles when the aspect ratio of the constituent carbon nanotubes is low. For high aspect ratios, the effects of these two factors are negligible. The influence of carbon nanotube waviness on electrical percolation thresholds has also been studied.