Finite difference solutions and observations have been presented for the flow of dilute suspensions of rigid, high aspect‐ratio fibers in Newtonian fluids through a 4:1 tubular contraction. The effect of flexibility of particles on the flow fields is also discussed from comparison of their configuration and entry flow patterns between rigid fiber suspensions and flexible molecule systems. For rigid fiber suspensions, the main flow patterns become nearly conical and the corner vortex length is almost independent of flow rate under the Reynolds number less than 0.1. On the other hand, for flexible molecule systems, the corner vortex rapidly grows with an increase in flow rate and the wine‐glass shaped flow with the convex vortex boundary also presents a striking contrast to the fiber suspension flows. Therefore, full discussion of the change in fiber or molecule configuration during flow seems most significant to understand the energy flow kinematics. Further, the computed stress fields clearly indicate that entry flows of rigid fiber suspensions can also exhibit the stress relief phenomenon due to vortex enhancement, which was observed for polymer liquids: the increase in the normal stress difference around the center line near the entrance of the contraction can be suppressed.