This paper presents three-dimensional simulation of fiber suspension flows in a cavity using the Finite Volume Method (FVM). The numerical simulation model described makes it possible to predict the propagation of the fiber-polymer solution and fiber orientation during the filling phase. Therefore, the objective of the work is to develop a Computational Fluid Dynamics (CFD) model to simulate and characterize the fiber suspension flow in three dimensional cavities. The model is intended to describe the fiber orientation distribution in three dimensional mold cavities. The continuity, momentum, energy and the fiber orientation equations are solved using the FVM. The flow is considered to be incompressible, non-isothermal, transient, and to behave as non-Newtonian fluid. A numerical analysis is presented to illustrate the application of the FVM to dilute suspension flows in injection molding processes. The volume-of-fluid method is employed to describe the flow of the two incompressible, immiscible phases, i.e., liquid suspension and air. Since the flow is a non-Newtonian, the Cross model is used to describe the shear-thinning behavior of the suspension. The governing equations of the flow and the fiber are implemented and solved by means of the open source code OpenFOAM. The evolution equation of the fiber orientation contains a fourth order orientation tensor which is approximated in terms of second order tensor through the use of appropriate closure rules. In this study the Hybrid closure model of Advani and Tucker is used to approximate the fourth order orientation tensor. To validate the numerical algorithm, test cases of suspension flow in a rectangular cavity are modeled for different fiber-polymer matrices. The numerical results are compared with available experimental findings and with those of Newtonian flows. Copyright © 2010 by ASME.