In common electroporators, cells can be transfected with foreign genes by applying a 150-700 V pulse on the cell suspension. Because of Joule heating, the cell survival rate is 10-20% in these elecroporators. In a recently developed electroporator, termed the low-voltage electroporator (LVEP), cells are partially embedded in the pores of a micropore filter. In LVEP, cells can be transfected by applying 25 V or less under normal physiological conditions at room temperature. The large increase in current density in the filter pores, produced by the reduction of cur-rent shunt pathways around each embedded cell, amplifies 1000-fold the local electric field across the filter and results in a high-enough transmembrane voltage for cell electroporation. The Joule heat generated in the filter pore is quickly dissipated toward the bulk solution on each side of the filter, and thus cell survival in the low-voltage electroporator is very high, about 98%, while the transfection efficiency for embedded cells is above 90%. In this paper, the phenomenological theory of LVEP is developed. The transmembrane voltage is calculated along the membrane of the cell for three different cell geometries. The cell is either fully, partially, or not embedded in the filter pore. By means of the calculated transmembrane voltage, the distribution of electropores along the cell membrane is estimated. In agreement with the experimental results, cells partially embedded in the filter pore can be electroporated by as low as 1.8-3.5 V of applied voltage. In the case of 25 V applied voltage, 90% of the cell surface can be electroporated if the cell penetrates further than half of the length of the filter pore.