It's 45 minutes to showtime at the People's Art Theatre in Beijing. Backstage, actors in civvies are padding around, studiously avoiding the clock. Behind a dressing-room door, someone is making heavy weather of their warmup. Suddenly, the strangulated squeal of an electric guitar shakes the building, like a crack of thunder. No one bats an eyelid.

The closest most British stagings of Shakespeare get to guitars is the occasional lute. But in China, it seems, they prefer their Bard a little gnarlier. This is The Tragedy of Coriolanus by Lin Zhaohua, routinely described as China's most controversial theatre director. First performed in 2007, it is big in every sense: there's a cast of more than 100, and the action takes place on a near-empty stage against a vast, blood-red brick wall.

But the real surprise is the soundtrack: two live heavy-metal bands, going under the colourful names of Miserable Faith and Suffocated, who slide in periodically from the wings and punctuate the action with frenzied surges of nu-metal. This might be the only version of Shakespeare's tragedy – the story of a hot-headed general who goes to war against his own people – that turns it into a battle of the bands.

The director is hiding in a cloud of cigarette smoke in the theatre cafe. Were it not for the translator hovering at his elbow, you'd mistake Lin for an elderly caretaker: a slight, somewhat caved-in figure, his jacket hanging absent-mindedly off one shoulder. But, behind neat spectacles, his dark eyes are pin-sharp. He claps me on the shoulder as I sit down; I sense I'm being sized up.

First things first: why the heavy metal? "I wanted to use rock music to display the fierceness of the war, and the rioting of the citizens," he says. "At first I wanted bands from Germany ... I listened to a lot of them, but I didn't like their electronic sounds. So Yi Liming, my designer, showed me around different parts of Beijing. I chose two of the bands I saw."

The music certainly adds a volcanic energy. The text has been translated into contemporary Mandarin, and here in Beijing (unlike at the Edinburgh international festival, where the show will open later this month) there are no surtitles. The scalding force of Shakespeare's verse, though, is echoed in the roaring guitars and pulsing bass. It's a high-voltage experience, particularly when the Roman mob, dressed in semi-druidic robes, rush onstage brandishing wooden staffs – like a cross between a scene from Star Wars and Reading festival. In the interval, the musicians entertain the crowd, a flock of teenagers pressing close, clicking away with their cameraphones.

Lin smiles. "Some dramatists and critics don't like the idea of using rock music, and they criticise my way of doing productions." How does he feel about that? A shrug. "I don't care."

Combing the city's nightspots for musical accompaniment sounds energetic for a director now in his late 70s. But Lin has never done things by the book. After graduating from the Beijing Central Academy of Drama in 1961, he joined the People's Art Theatre (BPAT) – China's equivalent of the RSC – as an actor, only to find his career stymied by the Cultural Revolution. Afterwards, he joined forces with the dissident writer Gao Xingjian, who would later win the Nobel prize. A trio of plays, beginning with 1982's Absolute Signal, all but launched experimental theatre in China, with a confrontational, often absurdist style that unnerved the communist authorities.

In the decades since, Lin has been prolific, flitting between new drama, stylised Peking Opera and ambitious reworkings of western classics. According to Li Ruru, an academic who has written extensively on Chinese theatre, Lin is "a major voice. He's been doing experimental theatre for more than 30 years, at the absolute vanguard of Chinese spoken drama." But his approach hasn't always done him favours: one critic described him and Gao as "harbingers of strangeness" for their efforts to release drama from the straitjacket of Soviet-era social realism. The director refuses even this pigeonholing: "I have no style," he has repeatedly told interviewers.

Anyone expecting peony-strewn chinoiserie – like that offered by the National Ballet of China two festivals ago – will be in for a shock. This is a Coriolanus of muscular clashes and brutal comedowns; of a leader always itching to administer the hair-dryer treatment, and who does nothing to disguise his detestation of the masses.

In the lead role is one of China's most famous stage actors, Pu Cunxin: a disconcertingly polite figure who apologies for his sore throat – the consequence of competing with two metal groups. "It is an unusual way of performing," he admits. "We don't normally have this kind of collaboration in China. The noise is just so powerful on stage, but we need the rock music to express these emotions. It parallels Shakespeare's ideas."

I'm struck by one moment in particular, where Coriolanus's arch-rival Aufidius grabs a microphone during a battle scene, looking half like a wannabe rock god, half like a politician channelling the energy of the crowd. Politics are everywhere in Coriolanus: the play has been claimed both by leftwing critics as a primer on the dangers of demagoguery, and by the right as a lesson in the fickleness of the masses (the Roman citizens at first swoon over their apparently invincible general, then later turn on him). Given these paradoxes, it feels an oddly appropriate play for present-day China, a country nominally communist, but with an economy many capitalists would trade their copies of Milton Friedman for. On the short walk from my hotel to the theatre, two blocks from the Forbidden City, I drift through a shopping district crammed with western luxury brands; one window of a photography shop is jewelled with glittering Japanese cameras, the other with portraits of Mao and Deng Xiaoping. It would be harder to find a clearer image of Deng's infamous "socialism with Chinese characteristics".

What does Lin see in Shakespeare's text? "The relations between the hero and the common citizens," he replies. "In ancient Rome, people admired heroes. From my point of view, Coriolanus is a hero." Is there a resonance with contemporary China? "It's a good phenomenon if the play refers to current events. Those in power like to control citizens, and some common citizens are foolish."

I want to find out about a previous Shakespeare production, Lin's Beckettian staging of Hamlet, first seen in 1989. Performed in a rehearsal room at BPAT, the only prop a barber's chair, it had three actors (one of them Pu) sharing the roles of Hamlet, Claudius and Polonius. Depending on your perspective, it captured either capitalist alienation, or the disillusion that followed the collapse of the student protests at Tiananmen Square. The parallels were cloudy – theatrical censorship is vigorously alive in the People's Republic – but there to be seen.

Lin freely admits the show was unusual: in contrast to the traditional Chinese way of presenting Shakespeare, with wigs and western-style makeup (sometimes even prosthetic noses), his actors wore their own clothes, in a conscious decision to show the student prince as just another guy. But he is reluctant to open up on the wider issues. "I hate politics," he says stoutly. "Hamlet has nothing to do with politics. It's just about a person's situation." I can't tell whether he's genuinely uninterested, or unwilling to be frank with a British journalist. "I never discuss politics. I don't think you can direct a production just from politics." He isn't even convinced, he says, he's avant-garde. "I don't have that concept. I just direct the production from my interests and from the needs of the play."

Our time is nearly up; his lighter is snapping impatiently. Last question: does he like being called a rebel? "I don't have preconceptions about what I'm going to create," he stonewalls. "I just follow my instincts."

I realise as I'm rushed out that I've forgotten to ask one thing – why direct Shakespeare in the first place? Why stage reach for a playwright four centuries old? When I email, the answer comes back quicker than I expect. It reads: "It gives me the freedom to say what I want."