Recent advances of robot technology raise increasing demands for tactile distribution sensor for safe and natural human-machine interaction. For a richer variety of tactile interaction, and for realizing a full surface coverage of various structure robots, not only flexibility, but also stretchability is very important. However, stretchability has been an impossible characteristic due to circuit wiring networks embedded in the sensors. This paper presents a tactile distribution sensor based on inverse problem theory. It solves the wiring problem and realizes a novel stretchable tactile distribution sensor, with potentially a broad range of functionality and applications. EIT, an inverse problem theory, can estimate the resistivity distribution of the inner space of a conductor, by measuring only from the boundary of the conductor. By applying EIT to a force sensitive resistive rubber sheet, a flexible, stretchable and thin tactile distribution sensor is realized with no embedded wiring within the sensing area. To verify the basic characteristics and potential of the EIT-based sensor, experimental results on pressure distribution and stretch dis-tribution sensors are reported. Morever, we propose a porous stretchable sensor with novel tactile sensing capability; pinching, rubbing and pushing. Proposals on possible augmentations of the sensor are also presented, including a construction technique for various sensitive conductors, a multi-layered sensor for multi-stimulus perception.