We report process simulations of molecular orientation of liquid crystalline polymers for isothermal channel flows in extrusion. The simulations use a "polydomain" model due to Larson and Doi (Larson and Doi, J. Rheol., 35, 539 (1991)), which is implemented by exploiting a nearly exact analogy with a fiber orientation model that is widely used for analysis of composites processing. Simulation results are compared to experimental data previously obtained using a customized X-ray capable extrusion die that allows a wide range of channel flow geometries to be explored. Competition between inhomogeneous shear and extension in these kinematically complex flows has a profound effect on the resulting molecular orientation distributions. We find that the Larson-Doi model successfully predicts most aspects of the experimental observations, demonstrating its utility for process modeling. POLYM. ENG. SCI., 48:2258-2269, 2008. (C) 2008 Society of Plastics Engineers