An isolated cochlear outer hair cell can elongate or shorten when electrically stimulated, as discovered by Brownell et al. [Science 227, 194-196 (1985)]. In their experiments, the cylindrically shaped cell was fixed at one end, and was positioned between two electrodes which lie on the cell axis, but were far from the cell (transcellular stimulation). A model is developed to predict the component of the cell's elongation which arises from only electrokinetic phenomena. Outside the cell, electro-osmosis produces a drag on the lateral wall which almost exactly balances the electrophoretic force. In contrast to previous theories, we find that the electrokinetic response is governed by the free end of the cell, not the lateral wall. If the surface charge density of the free end lies between -0.004 and -0.07 C/m2 (corresponding to the zeta potential between -5 and -60 mV), then our model predicts elongations that are comparable in magnitude to experimentally measured values.