Viscoelastic flow at a region of a circular pipe entrance was examined numerically. The numerical calculation was achieved by using I.C.E. (implicit continuous‐fluid Eulerian) technique with the K‐BKZ type constitutive equation. The transient flow characteristics with the sudden stand‐up were obtained. The resultant flow field and its associated flow parameters of the K‐BKZ integral constitutive equation were compared with the Newtonian case and the Oldroyd‐B model. It is revealed that flow is largely affected by a choice of the Deborah number. When the Deborah number is high enough for a fixed Reynolds number, there would be a circulation zone at the entrance region of the pipe by the effects of the viscoelasticity, which cannot be observed with the Newtonian flow.