Nonconducting liquids and biofluids, such as oil, ethanol and blood, cannot be pumped directly by electroosmosis, but still can be dragged along by shear forces of a neighbouring conducting liquid which is driven by electroosmosis. This method now has become a new method of electroosmotic pumping in the field of Lab-on-a-chip or micro Total Analysis Systems (mu TAS). The paper presents a numerical scheme for a circular two-phase electroosmotic flow. The conducting peripheral layer is pumped by an electric field, while the inner layer is dragged along by the conducting layer's viscous forces. Analytical solutions of the electric potential distribution, velocity profile, flow rate and electric current are obtained based on reasonable assumptions and simplifications, It is found that the two-phase flow characteristic mainly depends on the peripheral layer's properties. The theoretical results are helpful for designing this type of micropump. (C) 2009 Elsevier B.V. All rights reserved.