The rheology of a discontinuous fiber filled polypropylene in squeeze flow between parallel plates is studied. The material has an initial anisotropic fiber orientation distribution and therefore displays a strongly anisotropic in-plane flow behavior with predominant flow transverse to the axis of principal orientation. The kinematic field is computed using a linear, orthotropic constitutive model, where the fibers are assumed to move affinely with the surrounding fluid. The fiber orientation distribution is updated in each timestep thus coupling orientation and flow. Two different orientation descriptions are evaluated: orientation tensors with closure approximations, and a technique based on direct solution of the orientation of a set of test fibers. The two methods are first compared to exact solutions of the orientation distribution function in simple shear and pure extension; the direct solution is exact within numerical error, whereas the methods based on orientation tensors and quadratic and hybrid closure fail to correctly describe any transient fiber orientation evolution. Finally, the orientation representations are implemented in the kinematic model and compared to the experimental data; the direct solution method is found to give a very accurate prediction of the observed flow kinematics, whereas the other techniques result in substantial errors.