Flow of viscoelastic fluids in annular geometry is of considerable industrial interest. In this study, the Giesekus model is used to obtain the solution for axial annular flow of a viscoelastic fluid. In the course of the solution, an approximation to radial normal stress estimation is proposed that results in an analytic expression for the velocity and pressure profiles, and its validity is examined by comparison to the exact solution during a parametric study. The restrictions on the solution are discussed and for 0 < alpha less than or equal to 0.5, no limiting value of De was found. To demonstrate the effects of material parameters, flow conditions and geometry, an extensive parametric study is performed. (C) 2004 Elsevier B.V. All rights reserved.