The PhyFlex project addresses the lack of flexibility in the control of Tangible User Interaction (TUI). On the contrary to previous work, this project addresses a new research question: universal and flexible physical control. PhyFlex opens new perspectives on TUI based on the flexibility provided by the dynamic change of shapes of input devices. Shape-Changing TUI consist of physical User Interfaces (UI) whose shape can be changed by the user or the system. For instance, a tangible knob can be reshaped continuously to increase its resolution when its diameter increases. Providing the physical flexibility of control that is lacking in TUIs could reshape the User Interfaces of tomorrow. In particular, in the critical domains where TUIs are widely and successfully used, the lack of flexibility costs money, usability, mobility and, sometimes, even security. As a consequence, the problem addressed by the project is a very important one. However, to provide physical flexibility to TUIs, the project will need to overcome several obstacles: (1) current knowledge lacks the fundamentals of interaction with physically flexible UI, (2) current HCI theories are inconsistent with physically flexible UI, (3) the design of efficient interaction techniques with physically flexible controls is an unknown area of HCI, (4) material and hardware technologies to build prototypes are not mature yet, and (5) current way of implementing interaction in software are inappropriate. The intended breakthrough of this project is to bring the flexibility of control to physical user interfaces through physical shape-change. Toward this goal, the project will devise a new theory for physically flexible User Interfaces. Exploratory User studies will unveil the opportunities and limits of physical shape-change to support flexibility of control. Interaction techniques will explore devices that change in resolution, definition, number of dimensions and range. Prototypes combining physical, hardware and software will be built. User studies demonstrating the benefits and drawbacks of prototypes will be conducted to feed the theory. Tools to build such user interfaces have yet to be invented, for the research community to take up the results as well as for transfer. The originality of our approach is fourfold: (1) We want to address the fundamentals of interaction instead of taking a technologically-driven approach, (2) We want to address the continuous flexibility of control through shape-change, (3) We want to address the challenges of computer science, (4) We want to ensure retro-compatibility with current interaction. Future applications are numerous, ranging from tangible controls for interactive visualization, mixing console, control of LED lighting, cockpit or camera control, etc. to personal computers. To achieve the objectives, the project brings together a CNRS researcher, coordinator of the project, specialist in Human-Computer Interaction with mixed physical-digital UI, as well as a team of nine young researchers (Researchers, Assistant professors, Master and PhD students and an engineer).