The electroosmotic flow in an elliptic channel having constant surface potential (CSP) or charge density (CSCD) is considered at low potential and arbitrary double layer thickness. Analytical expressions for the flow velocity and the corresponding asymptotic results for thick double layers that are readily applicable to experimentalists are recovered. For the range of salt concentration usually encountered in practice, the mean flow velocity for the case of CSP differs both quantitatively and qualitatively from that for the case of CSCD. Using an equivalent circular channel to simulate an elliptic one is inappropriate, in general, neither is assuming electroneutrality on the channel axis even when double layer is ca. 1/3 of the equivalent channel radius. (C) 2015 Elsevier Inc. All rights reserved.