Short-fiber reinforced polymer composites enjoy widespread industrial applications due to their high strength-to-weight ratios and versatile manufacturing processes. The mechanical, electrical and thermal properties of short- fiber reinforced composite systems are tremendously dependent on fiber orientations within the polymer matrix during the manufacturing process. However, the commonly used melt flow simulation tools employ simplified empirically-derived models that have recently been shown to over-predict the rate of fiber alignment. Therefore, a physical understanding of fiber suspensions during the injection molding process is critical. The main objective of this research project is to develop a systematic methodology to predict fiber orientations during the manufacture of polymer composites through the numerical simulation. The focus is to address such issues as the effect of fiber shape, fiber- fiber interactions, Brownian motions of nano- fibers and fiber suspensions in various solvents, such as inhomogeneous flows. We develop a stand-alone Finite Element Method (FEM) for calculating hydrodynamic forces and torques exerted on fibers. For nano- fibers, the Brownian forces and torques are modeled using a Gaussian distribution function. Our approach seeks fibers' velocities that zero the net torques and forces acting on the fibers by the surrounding bulk fluid. Fiber motions are then computed using a 4th-order Runge-Kutta method to update fiber positions and orientations as functions of time. The successful completion of this project provides a systematic computational approach capable of addressing issues that are currently unresolved in the critical area of manufacturing. Extension of the approach to other areas such as drug delivery and blood cell motion is an additional benefit of this research work.