An electrostatically driven peristaltic micropump is presented in this paper. A colloidal particle suspended in an electrolyte inside a charged cylindrical capillary will experience an electrical double layer force due to the charged capillary wall. Perturbations in the geometry of the capillary wall result in modification of the electrical force on the particle. If moving these perturbations of the capillary wall along its axis can set up a peristaltic motion of the capillary wall, it will drag the colloidal particle along the capillary. This type of motion can be employed to develop a microfluidic pumping device. This article describes a finite element simulation procedure employed to model such a device.