We report the results of a detailed numerical investigation of inertialess viscoelastic fluid flow through three-dimensional serpentine (or wavy) channels of varying radius of curvature and aspect ratio using the Oldroyd-B model. The results reveal the existence of a secondary flow which is absent for the equivalent Newtonian fluid flow. The secondary flow arises due to the curvature of the geometry and the streamwise first normal stress differences generated in the flowing fluid and can be thought of as the viscoelastic equivalent of Dean vortices. The effects of radius of curvature, aspect ratio and solvent-to-total viscosity ratio on the strength of the secondary flow are investigated. The secondary flow strength is shown to be a function of a modified Deborah number over a wide parameter range. (c) 2013 The Authors. Published by Elsevier B.V. All rights reserved.