The paper deals with the impact of non-linear viscoelastic fluid properties on the pumping characteristics of a peristaltic system. For this purpose, a fluid dynamical model characterized by a long tube filled with a highly viscous liquid and by a periodic wave train traveling along the flexible wall is studied theoretically. The wave shape may be arbitrary and is specified for illustration purposes only. A asymptotic analysis of the axisymmetric, periodic, creeping flow has been performed under the condition that the wavelength is large compared to the mean tube radius. Analytical findings show the influence of the aspect ratio, of the Weissenberg number, of the Deborah number and of the wave shape. They allow also recognizing that the velocity field and the stress field are influenced by the fluid elasticity in a different way. Symmetries observed with a Newtonian fluid remain valid within the approximation order as regards the kinematics of the peristaltic flow, but get lost concerning dynamic field quantities. Under the condition of free pumping at small wave amplitude, the volume flux generated by the traveling wave may be a non-monotonic function of the wave frequency at otherwise constant parameters. (C) 2013 Elsevier B.V. All rights reserved.