The significance of the Bagley capillary end correction factor and capillary die swell are analytically investigated for a fluid obeying the quasilinear Oldroyd rate type constitutive equation which incorporates the Jaumann differential operator. The Goddard and Miller integration technique is used, under the assumption that the fluid enters the capillary with a fully developed velocity profile, to invert the constitutive equation and to produce an explicit relation for the pressure drop in the capillary. The inlet stress field decay in the capillary is shown to produce both nonlinear die swell behavior and nonlinear pressure drop behavior with increasingL/D.The theory is substantiated, in part, with experimental results.