Abstract: In the molding process of fiber reinforced polymeric material, the flow residual stress caused by fibers impacts the performance of material seriously. The analysis of flow residual stress depends on the proper model which must include information of different scales. Here, a multi-scale model was used, in which the macro-flow, the mesoscopic fiber orientation and the microscopic polymer molecular chains were coupled together. In a contraction cavity, using the SIMPLER-FDMS (Semi-implicit method for pressure linked equations revised and finite difference method on source term) method, the fiber orientation and stress distribution of the fiber reinforced polymeric melt were analyzed. And the normal stress difference and shear stress of polymeric melt coupled with fibers or not were discussed. The results show that the fibers rotate periodically in the zone where the shearing motion is dominant, and the fibers orientate along a single axis in the stretched zone; as the fibers rotate periodically, the normal stress difference distribution of fiber reinforced polymeric melt appears unsteady coherent vortex configuration.