We present TUIC, a technology that enables tangible interaction on capacitive multi-touch devices, such as iPad, iPhone, and 3M's multi-touch displays, without requiring any hardware modifications. TUIC simulates finger touches on capacitive displays using passive materials and active modulation circuits embedded inside tangible objects, and can be used with multi-touch gestures simultaneously. TUIC consists of three approaches to sense and track objects: spatial, frequency, and hybrid (spatial plus frequency). The spatial approach, also known as 2D markers, uses geometric, multi-point touch patterns to encode object IDs. Spatial tags are straightforward to construct and are easily tracked when moved, but require sufficient spacing between the multiple touch points. The frequency approach uses modulation circuits to generate high-frequency touches to encode object IDs in the time domain. It requires fewer touch points and allows smaller tags to be built. The hybrid approach combines both spatial and frequency tags to construct small tags that can be reliably tracked when moved and rotated. We show three applications demonstrating the above approaches on iPads and 3M's multi-touch displays.