The advantages of the Generalized Eulerian-Lagrangian (GEL) formulations in modeling and numerical solution of unsteady flow of fiber suspensions are discussed. This formulation offers the flexibility of selectively applying an Eulerian (Spatial), a Lagrangian (Material), and any combination of these two frames of reference in the same computational domain. This flexibility offered by the GEL formulation is exploited to exactly determine the shape and location of the free surfaces and moving boundaries in the numerical simulation of various manufacturing processes. The application of the GEL formulation to the solution for the flow field and fiber orientation in the unsteady flows of dilute and semiconcentrated fiber suspensions are presented. The flow field and fiber orientation predicted by this method agree well with the available theoretical and experimental results.