Psychos, so they say, are the quiet ones - not frothy-mouthed maniacs, but suburban conformists with their shirts buttoned up to the top and their children locked in the cellar. If that's true, then psycho buildings are not the “Hey, look at me” museums of today's diva architects but the standard unit of the average British housebuilder, the one with the pitched roof and the little plastic windows. Because in architecture, as in life, a conventional façade can hide all manner of sins.

Psycho Buildings: Artists Take on Architecture, which opens at the Hayward Gallery on the South Bank in London tomorrow, aims to shake us out of any limited expectations that we have of our architectural surroundings. Ten artists who work with structures and spaces have designed large-scale installations, which radically alter your experience of the gallery building. It's a hugely ambitious exhibition that wants to slap us around and force us to become hyper-aware of space.

The catchy title is somewhat misleading. The show is not really about psychosis and architecture, although there are a few horror-movie moments; it's about subverting architectural norms. It was the title of a book of photographs by the German artist Martin Kippenberger depicting oddities that he noticed on his day-to-day travels. “They suggested an irrational or deviant architecture,” says Ralph Rugoff, the director of the Hayward, who curated the show. “I liked that idea.”

The exhibition is the centrepiece of the Hayward's 40th anniversary celebrations. Rugoff's inspiration for it was the gallery itself - in his opinion it is a psycho building in its own right. It looks like a government bunker for top-secret research. Designed by the architecture department of what was then called the Greater London Council (it's amazing how progressive local authority architects used to be), it is a landmark of Brutalism, the movement of the 1950s and 1960s with a fetish for exposed concrete. Sternly sculptural, Brutalism had a disciplinarian quality that the British public has never really warmed to, despite works of beauty such as Denys Lasdun's National Theatre next door.

A number of the artists in the show have used the building as a coat-hanger for their ideas. The Viennese collective Gelitin, for instance, has turned the western sculpture terrace into a boating lake. You don't get many opportunities in this city to row a boat 12 metres (40ft) above the ground while looking down at the river. This is precisely the kind of physically and perceptually incongruous experience that makes Psycho Buildings such a generous show. The Hayward clearly wants to get noticed. Last summer, the sculptor Antony Gormley decked its roofs with suicidal-looking figures; this summer, look up and as well as rowers you'll see a cinema made of scaffolding and people floating in a geodesic dome.

Roughly speaking, the show can be divided into two categories: works that propose new ideas of what architecture could be, and those that suggest alternative psychological readings of the architecture we already have. Put even more bluntly, you might say that it's divided into dreams and nightmares.

In the first category is Ernesto Neto's Life Fog Frog ... Fog Frog, a porous igloo-like structure made of the same material as ladies' stockings and supported by plywood dinosaur bones. Inside hang pendulous tonsils full of dark powder, which, when you get close, you discover is black pepper and cloves. It's not just an architecture of the senses, one that encourages us to touch and smell; it also appeals to our primal, animal origins. With some humour, the Brazilian artist seems to be suggesting that it is within our own skin and bones, our own wombs and orifices, that we'd be most at home.

Although they couldn't look more different, there are parallels in Michael Beutler's piece, which looks down upon Neto's from the mezzanine. The German sculptor has created a structure that is everything the Hayward is not: light, porous, colourful. With pliable mesh walls plastered in bright tissue paper, it evokes a shanty town but feels more like walking into an abstract expressionist painting.

Such are the liberties that artists enjoy when they create “architecture” in galleries: they get to make big things without any of the practical constraints of the real world. Which is why it feels nicely balanced to have two very good architects in the show creating something reassuringly solid.

Again playing off the building, the Japanese duo Atelier Bow-Wow have made a tunnel of steel plates that connects two galleries. It's only a short transitional space but Life Tunnel forces you to crouch, making you aware of your physical boundaries. Passing between its beautiful faceted walls is like entering a portal to another world, and, as in many of the works in the show, that world feels filmic - it's as though the ventilation shaft that Bruce Willis crawls though in Die Hard is leading to Kubrick's 2001: A Space Odyssey.

The treatment of architecture in the movies, or even the media, might well be the subject of Show Room by the Cuban collective Los Carpinteros. Using wires to suspend debris from the ceiling, the work captures what looks like a domestic interior in mid-explosion. In the wake of 9/11, the Iraq war or any of the recent natural disasters, this is a scene ripe with different readings but also one that you “get” instantly. It is as spectacular as it is banal: right now someone's home somewhere is being obliterated - look for it in tomorrow's paper.

Once you become attuned to them, the nightmares start to proliferate. There is a similar disaster unfolding in Fallen Star 1/5, one of two pieces in the exhibition by the Korean artist Do Ho Suh. It is a meticulous 1:5 scale model of his traditional family home crashing into the 19th-century townhouse in Providence, Rhode Island, where he lived as a student. With echoes of the cyclone in The Wizard of Oz, it's a literal snapshot of culture shock.

Rachel Whiteread's eerie Place is a sleepy town of doll's houses - well, either it's sleepy or it's abandoned, after some societal trauma. Here, in miniature, normality is made disturbing. And finally, there is Mike Nelson's To the Memory of H.P. Lovecraft, where at last the axe-wielding psycho you've been waiting for arrives on the scene. Nelson's installation looks as though the gallery has barely contained some raging force - lunatic, wild animal, poltergeist? These splintered walls suggest our own repressed violent potential.

You might say it's a dark show. The cultural barometers of many of these artists reflect an anxiety that is in the air these days. With half of the works either insinuating or explicitly depicting a cataclysm, it's no wonder the other half feel escapist. The final work, on one of the other sculpture terraces, is by the Argentinian Tomas Saraceno and consists of a dome designed by the visionary Buckminster Fuller in the 1950s, in the middle of which is a transparent PVC pillow. When you walk onto it, you will appear to those below you to be walking on air. This combination of an archaic vision of the future with a classic dream fantasy is either optimistic or deluded depending on how you want to read it. But it is also one of many rich experiences this show offers that you may never get again.

Justin McGuirk is the editor of icon magazine, www.iconeye.com

Psycho Buildings, from Wednesday until August 25 at the Hayward Gallery, London SE1 (0871 6632519)

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