A new flexible tactile sensor has been designed on the basis of the electric potential distribution of the planar steady current field. The sensor is built to detect information on the contact position for human–robot interaction, such as that involving human-care robots, medical robots, or other service robots. The design scheme of a three-circle conductive plane was proposed according to the refraction of electric field lines by comparing various schemes, which can realize the X and Y coordinate detection of contact positions. An approximately linear relationship between the potential distribution and contact position coordinates was verified through COMSOL simulation, and an error distribution rule for contact position detection on the conductive plane was deduced. Then, a design scheme of the tactile sensor with a three-layer structure was proposed; such a structure consisted of an upper conductive layer, a middle isolation layer, and a lower conductive layer. A mathematical model of contact position detection was established, and the influence of surface contact on detection accuracy was analyzed with COMSOL. A flexible tactile sensor sample was fabricated, and an experiment on contact position detection was conducted on the sensor sample. The feasibility of the sensor was verified with a robot manipulator.