It was a bright idea of the Saatchi Gallery to hold an exhibition of paper. It's such a wonderful, tactile material. The technology experts may say its days are numbered, and even in the art world, David Hockney has shown that you can as easily sketch a landscape on a digital tablet as on paper and then reproduce it at will. Little wonder that colleges are downgrading the subject of drawing, once the mainstay of formal art education. No surprise either that the futurologists predict a day when offices will do without it entirely.
Fine, but what does a parent do when they want to encourage creative play by their children other than hand out paper and crayons? And what do teachers in playgroups do to keep their charges involved better than put scissors and glue alongside paper to build edifices and scenes? The Japanese have the whole craft of origami, devoted to the art of folding paper into shapes. The festivals of Latin America, India and Europe have long used paper to make giant figures on floats. Old newspaper and flour-and-water have been for centuries the source of the grandest of sculptural fantasy.
It's no wonder then that the most entrancing exhibits from the 44 artists here are those nearest to childhood innocence. Yuken Teruya has assembled a series of paper carrier bags, snipped one of the sides to make cut-out drop-down trees and stuck the bags by their bottoms on the walls. The result is a line of peep-shows as you look inside to see the trees in the colours of the paper. In curatorial-speak you could no doubt make much of the fact that these are disposable items made from wood pulp and carved into figures of their origin – layer upon layer of meaning. In reality the skill and the imagination are just enchanting.
The same could be said of Han Feng's Floating City. The "city" is made up of tissue-paper buildings suspended by fishing wire a few inches above the floor. They float and sway, massed in their square precise outlines but white and weightless in the air. You could go on – and the curators do – about how all this represents the ephemeral nature of modern urban living and the mirage that is our built environment. Or you could just look at the installation with the eyes of a child, wondering at the grace and the delicacy of this work of imagination.
Maybe it is because Teruya and Feng are both Asians (Teruya is Japanese, Feng Chinese) that they seem so at ease with the material and prove so playful with it. You are never far in Asian art from nature and its fragility.
The sculptural efforts of the Western artists on display here are much more direct. The Brazilian Marcelo Jacome expands on one of the most basic of all paper structures, the kite, to erect a giant sculpture of geometric shapes that fill an entire gallery. What makes it work is not just the sense of jumbled confusion of cubes and triangles pushing at each other, but the primary colours with their strong associations of wrapping paper and presents.
The joy of paper is that you can take a two-dimensional sheet and make it into a three-dimensional object, bulky but void. Rachel Adams uses crumpled paper to create bronze-like forms, with all the force of metal but not its mass. Jodie Carey uses newspaper stained with coffee, tea and blood – with titles such as The Daily Mail – Arrangement One and Arrangement Two – to make the most exquisite sprays of flowers. Rebecca Turner in Dumbstruck has fashioned a paper pulp ball that floats halfway up the wall like a balloon, only seemingly solid. The Spanish artists José Lerma and Héctor Madera honour the boxer Emanuel Augustus, with a gigantic paper bust. Tom Thayer makes paper cut-outs of birds in an effort to capture their lightness and elegance while Jannis Varelas creates outsize collages of figures in what resemble maid's uniforms.
There are some fine graphic works. The Californian Zak Smith has painted complex compositions with acrylic and metallic ink at once erotically teasing and angry. Dawn Clements draws narratives of train journeys and domestic interiors, while Nina Katchadourian uses paper towels in aircraft lavatories to make headdresses and collars, and photographs herself wearing the results in the style of Flemish Renaissance portraits. Annie Kevans focuses on historical monsters, including Hitler and Saddam Hussein, and re-imagines them as the young child they might once have been.
If there is a disappointment in this show it is that so few of the artists here seem interested in the properties of paper itself. There's nothing intrinsically paperly about many of the works here.
Of all the works only those of the Frenchman Eric Manigaud, who transcribes historic photographs on to paper using pencil and graphite, and Austrian Klaus Mosettig, who uses a slide projector to create abstract patterns on rough paper, seem to explore the surface qualities of the material. Manigaud does it by sizing up old photographs of the patients of Nazi experimentation and Allied bombing and recreating them with pencil at life size. The effectgives the images the grainy reality of a magnified print but with the precision and force of the drawn line. Mosettig achieves his effect by projecting the minute imperfections of the lens glass on to the paper for his drawing, giving it the tentative quality of the almost imperceptible.
There's nothing very new in this, of course. Manigaud works in the tradition of Gerhard Richter, Mosettig in the style of Italy's Arte Povera. It's still effective but one misses the sense of daring in many of these works. There's a conscientiousness and skill but all too often a contentment with ironic self-reference. It's there, as ever, in the punning and allusive titles; it's a tendency which Saatchi seems drawn to.
But in the end one can't help but feel that it's a way of avoiding risk. Compare these works with the collages made by the American abstract artist Robert Motherwell in the 1940s and 1950s – currently on display at the Guggenhim in Venice – where he uses the papier collé technique of layering pasted paper to express his vision of a fractured post-war world, and you can't help feeling that the new generation has become rather too polite for its own good.
The result is a show conventional in its manner and playful in its mood. It's an exhibition to enjoy in the white-walled spaces that Saatchi has managed to carve out of the former barracks building in Chelsea, but not one which is going to change the way you look at the world or yourself.
'Paper', Saatchi Gallery, London SW3 (saatchigallery.com) to 29 September