In extruding a Newtonian fluid from a duct, the pressure at each position of the duct increases with increasing flow rate. In the case of viscoelastic fluids, the pressure near the duct exit decreases with increasing flow rate when the flow rate is higher than a certain value. In this study, we determined the velocity profiles near the exit of two-dimensional ducts for a 3% aqueous solution of polyacrylamide (Separan). With the use of observed velocity profiles and the constitutive equation of Denn, we evaluated the pressure distribution in the duct. It was revealed that the transformation of the elastic energy, stored at the duct entrance, to pressure in the duct becomes less effective with increasing flow rate above a certain flow rate. This ineffectiveness of the transformation may be the origin of the abnormal behavior of pressure near the duct exit.