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During processing of carbon nanotube (CNT)/polymer composites, materials are exposed to significant deformation that changes the microstructure and affects the properties of the final products. In order to improve the material properties and manufacturing process, a clear understanding of how these materials react to the flow fields is required. Single carbon nanotubes cannot be observed during processing with commercial characterization methods. Therefore simulations are the only way to get insight the movement of the carbon nanotubes in polymer melts. In this thesis, fiber-level simulation technique is employed to simulate CNT/polymer composites in simple shear flow. This model incorporates CNT flexibility, irregular CNT equilibrium shapes and CNT interactions. The combined effects of carbon nanotube properties such as aspect ratio, curvature and tunneling length, as well as shear rate on the microstructure and electrical conductivities of CNT/polymer composites are investigated. Electrical conductivities are calculated using a resistor network algorithm.