The creators of the prototype interface, called Obake, describe it as a "2.5D display".
Obake (named after a shape-shifting creature from Japanese legend), has been created by Dhairya Dand and Rob Hemsley of MIT's Media Lab.
The idea is to create an interface that can be literally contorted to create new styles of gestures to control devices, and add a 3D element to more traditional gestures, such as pinch-to-zoom.
Obake uses a silicon screen as its touch interface, while sensors and cameras monitor the pull and pull depth and actuators hold the shape of the distorted silicon.
It's very much a concept device, but it opens interesting new possibilities for how we could control devices.
The video embedded below shows how the interaction between Obake and a user works.