Dividing cells within living tissue that contain polarizable intracellular members can be destroyed using at least two insulated electrodes and an electric field source that applies an alternating electric potential across the conductors within the insulated electrodes. The electric field is transformed into a non-homogenous electric field that produces an increased density electric field in a region of the dividing cells. The non-homogenous electric field is of sufficient intensity to cause the intracellular members to be drawn to that region, which causes a pressure increase that results in a structural breakdown of the dividing cells.