An analytical solution is derived for the steady state, laminar, axial, fully developed flow of a viscoelastic fluid obeying the Giesekus model without any retardation time in a concentric annulus An approximation is used for the estimation of radial normal stress The influence of Deborah number (De) and the mobility factor (alpha) on the velocity profile, axial pressure gradient are investigated and results show strong effects of mobility factor and Deborah number on above parameters (c) 2010 Elsevier B V. All rights reserved