The axisymmetric Poiseuille flow of a purely viscous generalized Newtonian fluid under rate of flow controlled conditions is studied with a change in the boundary conditions at a transition point from an adhesive to a slip condition with friction at the wall. The friction law used originates from an experimental study by (J.M. Piau and N. Fl Kissi, J. Non-Newtonian Fluid Mech. 54 (1994) 121-142) using a capillary made of steel and a silicone fluid, and is based also on a molecular dynamics theory by (Yu B. Chernyak, A.I. Leonov, Wear, 108 (1986) 105-138). It gives a non-linear multivalued dependance of the wall shear stress to the velocity at the wall. Moreover, wall shear stress Values may become smaller than values obtained when adhesion prevails in the capillary. The shear stress must over-step some limiting stress level to trigger the wall slip. After checking slip boundary condition implementation for the case of Poiseuille flow with slip along the entire wall, the convergence and the validity of the computation was studied. Important morphologic changes of the flow field and the stress field appear around the transition point from adhesion to slip boundary condition. Slip at the wall allows the principal stress difference to be drastically reduced, except in the vicinity of the transition point where this difference is maximum. A peak in shear stress located upstream of the transition, and a peak in elongational stress located downstream of the transition, are observed at the wall. Fully developed near plug-like flows are obtained within about 1D only downstream of the transition point. It is concluded that the effect of slip on extrudates distorsion should appear clearly even when the exit slippery zone is reduced to 1D.