An alternative approach for solving unsteady flows of fiber suspensions and predicting the implied fiber orientation is discussed. The approach uses the traditional orientation tensor representation for describing suspensions flows but approximates them using finite deformation tensors. Using this approach, the stress tensor given by the theory used by Lipscomb et. al. [I] for dilute suspensions and Dinh-Armstrong theory for large aspect ratio fibers is expressed in terms of the Finger and Cauchy tensors using the Currie approximation. A semiimplicit finite difference scheme is then used to express the Finger and Cauchy tensors in terms of the kinematics of the flow. The proposed method has the advantage that it does not require any closure approximation as in the case of the traditional approach. Moreover, since the stress tensor is expressed in terms of the kinematics of the flow explicit solution for the solution for the components of the orientation tensor are not required. This reduces the computational time and storage requirements.