The unsteady viscoelastic flow generated by the sudden application of a constant flow rate is experimentally examined for an abrupt contraction and a tapered one with a rectangular cross‐section. The velocity change with time is measured with a L.D.V. for a 1.0 wt % aqueous solution of polyacrylamide. The gentle overshoot in the centerline velocity, which may be due to the effect of extensional flow, is observed from the vicinity of the entrance of a small slit to the downstream far from the entrance. Furthermore it is found that the flow in the entrance region finally reaches the anomalous three dimensional flow with a dual peak form of the velocity profile.