Current short fiber polymer composites processing models that predict fiber orientation are based on Jeffery’s pivotal 1922 work for single ellipsoids suspended in a moving fluid. Recently these models have been shown to over-predict the rate of fiber alignment and, unfortunately, little attention has been given to the underlying Jeffery model and how its assumptions affect orientation predictions. This paper develops a numerical approach for predicting the motion of a fiber or a set of fibers suspended in a moving fluid. Our approach is to evaluate the flow around a single fiber using the finite element method where the flow domain surrounding a fiber(s) is discretized and the velocity on the fiber surface(s) is defined in terms of known fiber centroid linear and angular velocities. Velocities on the outer boundary of the flow field are defined by a far-field flow function in a manner that is consistent with Jeffery’s work. The Newton-Raphson method is used to iteratively compute the translational and angular fiber velocities that zero the force and torque on each fiber. Then a fourth-order Runga-Kutta solver is employed to compute the fiber’s orientation and position at each time step from the converged fiber velocity results. Calculations show that fiber shapes other than ellipsoids have reduced hydrodynamic aspect ratios and tend to rotate more quickly than ellipsoids. The opposite is seen when two fibers placed near each other translate and rotate together as a cluster with a longer period. It was also found that a fiber in a quadratic flow tends to rotate more quickly as viewed with respect to location along the flow direction. Again, the opposite is true for a fiber having a far-field boundary condition placed near it which rotates more slowly than Jeffery’s model predicts. These results provide insight into the effect that basic assumptions made by Jeffery have on fiber orientation predictions for short fiber polymer composites.