The stress singularity for Phan-Thien-Tanner (PTT) and Giesekus viscoelastic fluids is determined for extrudate swell (also termed die swell). In the presence of a Newtonian solvent viscosity, the solvent stress dominates the polymer stresses local to the contact point between the solid (no-slip) surface inside the die and the free (slip) surface outside the die. The velocity field thus vanishes like r λ 0 , where r is the radial distance from the contact point and λ 0 is the smallest Newtonian eigenvalue (dependent upon the angle of separation between the solid and free surfaces). The solvent stress thus behaves like r −(1−λ 0 ) and dominates the polymer stresses, which are like r −4(1−λ 0 )/(5+λ 0 ) for PTT and r −(1−λ 0 )(3−λ 0 )/4 for Giesekus. The polymer stresses require boundary layers at both the solid and free surfaces, the thicknesses of which are derived. These results do not hold for the Oldroyd-B fluid.

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