The interest in the theoretical investigation of the flow behavior of fiber suspensions during manufacturing processes has increased considerably due to the increased interest in the use of composite materials. The unsteady flow of semi-concentrated fiber suspensions in two dimensions is investigated using the Generalized Eulerian-Lagrangian (GEL) formulation. The integral constitutive relation proposed by Dinh and Armstrong is used to express the stress tenser. Currie approximation is then used to express the integral expression using a differential expression involving the finite deformation (Finger and Cauchy) tensors and their invariants. A semi-implicit finite difference scheme is developed which expresses the finite deformation tensors in terms of the kinematics of the flow. The evolution of fiber orientation is also likewise expressed in terms of the flow kinematics. In order to determine the accuracy of the semi-implicit finite difference scheme, numerical results are compared with exact analytic solutions for a radially diverging source flow. The numerical efficiency and ease of implementation of the method are discussed. The method is then used to simulate the filling of a simple two-dimensional injection molding cavity.