This paper demonstrates a three-dimensional, non-linear, AC electro-osmotic extensional flow induced by the capacitive charging of a face-to-face pair of planar electrodes. These two planar electrodes facing each other had different sizes and shapes. The extensional flow was attributed to the rectification of the stagnation-point flow in the center region by the three-dimensional vortices at the corners of the smaller electrode. The measured flow velocity near the edge of the electrode was on the order of millimeters per second. The shape of the electrode affected the distribution of the electric field and thereby modified the electro-osmotic flow. A change in the shape of the smaller electrode would significantly affect the flow fields and could cause a variation of a factor of 10 in the measured flow velocity. An equivalent electronic circuit of the experimental apparatus was developed. Based on the equivalent electronic circuit, the calculated critical frequency was in good agreement with the measured optimal velocity frequency. The quadratic dependence of the velocity on the voltage drop across the liquid, a characteristic of the capacitive charging process, was also reported in this paper.