In this paper we study the axisymmetric flow of polymer solutions in a circular pipe. We use a rheological model which contains an evolution-diffusion equation for the microstructure. The justification of this new equation was introduced in a preceding paper Drouot and Berrajaa, Int. J. Engng Sci. 31, 1463 (1993). The diffusion term allows for the existence of a boundary layer near the wall and it gives a contribution to the slip velocity in certain circumstances. First we give the solution of this problem for the microstructure evolution without diffusive terms. This allows us to postulate some conditions. Then we write governing equations in dimensionless form and introduce three non-dimensional numbers. We are essentially interested in the situation where the microstructure influences the flow near the wall. We also studied the influence of boundary conditions on the volumetric flow rates and attempted to introduce the notion of “slip velocity”.