Flows of liquid crystalline polymers through parallel plates containing a cylinder are simulated using the modified Doi equation proposed by Doraiswarmy and Metzner. The flow domain is mapped onto a square one using a boundary-fitted curvilinear coordinate system, and the flow problem is solved with a finite difference method. The scalar order parameter depends significantly on the region at large Deborah numbers. The director pattern is similar to the results obtained for the TIF model only at low Deborah numbers. The disturbance of the molecular alignment due to the diverging flow remains far downstream from the cylinder. Furthermore the occurrence of a long weldline is predicted.