The extended Rouse-CCR tube model for linear entangled polymers recently proposed by the authors (Kabanemi and H,tu, J Non Newtonian-Fluid Mech 160:113-121, 2009), designed to capture the progressive changes in the average internal structure (kinked state) of polymer chains, is here used to analyze, by means of a time-dependent three-dimensional finite element method, chain segment dynamics, pressure drop, and stability of flow through a 4:1:4 constriction in a tube. The model predicts an enhancement of the pressure drop in the stretch-dominated flow regime, which is also observed experimentally. This excess pressure drop was not associated with the onset of flow instability. The model also predicts kinked configurations within chain segments in the entry section to the constriction tube, at the inception of flow, and prior to the development of upstream vortices. It is also shown how these kinked configurations within chain segments influence pressure drop transients.