FORTUNE — We are already pretty intimate with our smartphones, poking and swiping their screens almost without second thought. Now a Japanese phone maker is making the case we go a step further, literally squeezing and pinching them to do our bidding.

The country’s biggest mobile carrier, NTT Docomo, showed off a mobile phone in Tokyo recently that responds not only to the usual screen touches but also to pressure applied at its edges. They call it Grip UI.

The idea is to make controlling a smart phone easier with one hand, while, for example, hanging by one hand from a pole on the subway. It is the latest in a range of emerging technology haptic gadgets — and even bendable phones — that promise commercialization soon and that exploit our innate love of manipulating tactile, responsive objects. “Pressure sensitivity is a very interesting direction for phones so this is great technology,” says Ivan Poupyrev one of the world’d leading researchers into haptics at Disney’s (DIS) labs in Pittsburg.

Docomo’s Android-based mobile has 270 sensors embedded into the body of the phone allowing its user to execute at least four useful operations just by squeezing the bezel. Gripping the side of the smart phone with all five fingers will unlock the screen from sleep mode, for example. While pinching the sides at the middle with two fingers is equivalent to pressing the ‘back’ button. “For the icons you can’t press, you can grip instead,” explains a demonstrator at the phone’s first outing at a Tokyo trade show.

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Docomo doesn’t know when the phone might go into production. But malleable gadgets, like this one, could have other useful applications. Being able to control any hand-held with a squeeze of the fingertips is just a start says Poupyrev who teamed up with a German designer Carsten Schwesig and Japanese designer Eijiro Mori, to build one of the world’s first prototype flexible electronic devices for Sony (SNE) a decade ago. They were investigating the unique concept of a bendable credit-card-sized device nicknamed Gummi.

To make a click you just grasped it with two hands and bent it. It became the model worldwide for potential flexible phones such as Nokia’s (NOK) “Kinetic” prototype that debuted last year. The Nokia phone uses flexible organic light-emitting display (OLED) technology developed by Samsung — a technology it says it will bring to market early 2013. The idea is exploit the flexibility inherent in these recently commercialized thin, organic screens.

So far the most advanced flexible OLED screens are so thin, about the width of a human hair, and so flexible the color display can be rolled around a pencil while streaming video.

Future applications might include combining bendable electronics as manufactured by British firm Plastic Logic or a flexing phone made from electronic paper created by Canadian researchers at the Human Media Lab at Queen’s University dubbed paperphone. When bent or folded at its corners or sides the differing functions of a smartphone are brought to light say the researchers.

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Devices using haptics, or the science of touch, are about to transform the way we interact with just about anything electronic says Poupyrev who is working with Disney now on several haptic applications. “We don’t do enough with touch,” he argues. “With feel-able devices we can redesign the interface. All designers hate buttons. To have something replace them would be the ideal.” So far the designer has come up with not only a concept for touch screens that respond to bending but also those that are fully rigged, ‘feel-able’ graphic interfaces that push back.

The big question that remains he says is how to design effective gestures and interfaces that could take advantage of the enhanced sensitivity shown by the Docomo phone. Touch-based technology as around for years before Apple (AAPL) release the iPhone’s slick interface.

He suggests bendable media cards that could take the form of city maps or mini photo albums, making flicking through them as easy as flipping through the pages of a book, maybe easier. “The point is, however is that everyone is focused on making the materials, for example, on flexible electronics or displays. Very few people are looking into how these devices can be used and what are the killer, unique apps for these devices. Basically, everyone assumes that when devices appear the applications will follow,’ says Poupyrev. He thinks for a moment, then adds, “But we do not want to wait.”