Extrusion rheometry experiments with a commercial thermotropic liquid crystalline copolyester show concave Bagley plots and convex pressure profiles. A loss of the orientation produced at the entrance of the capillary and the slit can explain these non-linearities. Assuming that the order parameter, S, relaxes exponentially with time, the Doi-Edwards model for the shear flow of rod-like polymers is used to adjust experimental data.