Some new (boundary‐element) computations of the flow over a slot are reported. By studying the Maxwell model, we find the hole pressure effect is−0.24N1for this case, which is close to the−0.25N1result for a second‐order fluid. We believe this accurate result at low Weissenberg numbers is due to the use of tractions as primitive variables in the calculations; this avoids the need to add separately the pressure and extra stress tensors as is usually the case in other numerical methods. Using a modified Phan‐Thien‐Tanner model we were able to perform computations which are a very good fit to the experimental data of Pike and Baird for polystyrene. Various parameters were changed in the MPTT model, and we confirm the approximate validity of the Higashitani‐Pritchard analysis.