In the present work, a second grade fluid flow in a cylindrical tube is investigated. The perturbations were expanded in terms of the second order material coefficient, which means that either the second order parameter is sufficiently small or the characteristic diameter is very large. After obtaining the solutions for the impermeable tube, problem is examined for suction or injection through the surfaces of the tube. The general solutions are obtained for a tube of circular cross-section and also applied to a tube of arbitrary cross-section by using conformal transformation. (c) 2005 Elsevier Inc. All rights reserved.