Opera directors are always looking for new ways of presenting what are usually very old pieces. But almost certainly you will never have seen an opera done as Monteverdi’s The Return of Ulysses is about to be done at the Edinburgh Festival.

Yes, there are singers on stage. But they are not singing to the audience. “We auditioned for ages to find singers capable of not looking at the spectators!” the director, William Kentridge, says. “The whole concept and credibility of the show falls apart if they do.”

Instead they look at the figures who are presenting the action. And these are not actors but giant puppets, manipulated with skill and no little stamina by members of the South Africa-based Handspring Puppet Company. This is the company enjoying huge success in London with its spectacular contribution to War Horse, the National Theatre production of Michael Morpurgo’s touching children’s story about a horse sent into battle in the First World War.

“At some points, both in War Horse and in Ulysses, you are holding 70kg of wood above your head for minutes at a time,” says Basil Jones, Handspring’s co-founder. “The opera’s closing duet, when Ulysses is finally reunited with his wife Penelope after his journey, is exhausting for me and Adrian [Kohler, Handspring’s other guiding light]. We have to pump weights to prepare for it. You can’t say to an audience halfway through: ‘Sorry, but I’ve got to take a break because my arms are killing me.’ ”

So besides the singers and the puppets, lovingly carved by Kohler (“two weeks a puppet, usually,” he says) the stage for Ulysses will also be crowded with puppeteers as well. Won’t this be confusing for the audience? On the contrary, Jones says. He believes that the “triangulation” of each role (singer, puppet and puppeteer) draws people into the work. “Remember that this is a very old myth, retold in an opera that is itself nearly 400 years old,” he says. “For a modern actor to play such ancient figures as Ulysses and Penelope is a very big stretch. Those Ancient Greek heroes come from a world that is so distant from ours. But to represent them sculpturally, in puppet form, helps ease the audience’s imaginations into a mythic way of thinking.”

“More generally,” Kohler adds, “when a puppet does a very small gesture well — such as reaching forward and drinking from a cup — it reinvents that gesture in a way an actor cannot. It gives it an epic quality and we see it afresh. Often when adults come to a puppet show for the first time they say, ‘It was like being a child again.’ That’s because they are seeing gestures as if for the first time, as a child does.

“And generally, puppets can also remind you of just how difficult everyday life can sometimes be, especially if you are ill or old,” Jones points out. “We can empathise with the trouble they have accomplishing even the simplest tasks.”

It’s this aspect — the fragility of bodily existence, the vulnerability of the human condition — that is emphasised in Kentridge’s treatment of the opera. Another South African, Kentridge’s first vocation is visual art: he specialises in animated charcoal drawings. These are continually incorporated into his staged productions as scene-setting backcloths, and then often re-used in his gallery exhibitions.

But for Ulysses he also uses extraordinary footage of internal medical processes — X-rays, CAT scans and angiograms, many supplied by his wife, who is head of the rheumatology department at Johannesburg General Hospital. “It struck me that the character of Ulysses has a double nature,” Kentridge says. “He is heroic and vulnerable. That’s clear from the prologue to Monteverdi’s opera, where the gods discuss what his fate will be. Then he is discovered unconscious, and his first question is ‘Am I alive or dead?’ ”

All this suggested to Kentridge a man at the end of an exhausting life, in an extreme state of vulnerability. So he has set the work in a hospital, with Ulysses lying on a bed, clearly dying — and remembering, or perhaps imagining, his epic odyssey and his return to his beloved Penelope. The voyage itself is reconceived not as a geographical journey but an internal one — inside Ulysses’s own body. “In the opera there are references to the power of Jupiter’s thunderbolts,” Kentridge says. “Well, we are no longer frightened of thunderbolts from the gods. But we are terrified of internal thunderbolts, such as heart attacks. So by incorporating this medical imagery into the drama, we are reinterpreting Ulysses’ vulnerability in modern terms.”

Besides, Jones says, the imagery is itself both mysterious and mesmerising. “William’s friend had a stomach operation, so when you see a film of a trip down a human throat, it is his friend’s throat being filmed. But it also looks like a great black tornado. And images of liquids flowing inside the body, are beautiful, sensual, even erotic.”

Kentridge’s boldest stroke of reinterpretation, however, comes at the opera’s conclusion. At the very moment when the puppet playing the “heroic” Ulysses finally embraces Penelope, an attendant pulls a sheet over the “vulnerable” Ulysses, lying on the hospital bed. His reverie is over; he is dead. “And dying is something that puppets can do better than any actor,” Kentridge says, “because when the puppeteer takes his hands away, the puppet is just an inert piece of wood.”

Ulysses is Handspring’s fourth collaboration with Kentridge, but their only opera together. It has already been seen in South Africa, New York and on mainland Europe. But sadly the puppeteers have had to make some heavy cuts to the score. The whole thing now runs for 90 minutes rather than the usual three hours. Sub-plots and minor characters have been ruthlessly purged. “The Monteverdi purists were a bit enraged,” Jones admits. “But doing it complete would have killed us as puppeteers.”

Jones and Kohler founded Handspring almost 30 years ago, initially to entertain children. “We bought a truck and travelled all round Southern Africa, taking our shows into schools,” Kohler says. “That was our training in theatre, because both of us had been to art college, not drama school. We did our first adult show in 1985, and after that we started working with theatre directors who were keen to incorporate puppets into their productions. Our first show with William Kentridge was Georg Büchner’s play Woyzeck, transposed from Germany to a South African mining environoment.”

At the start, all the members of the company did everything, from making and manipulating the puppets to driving the truck and flogging tickets. “But the fact that Adrian’s mother was a puppeteer, and that he had spent his boyhood making puppets, meant that he was so much better at it than the rest of us,” Jones says. “So slowly I took on the producer’s role, and he became the artistic director.”

Both still perform, but for how much longer? Moving heavy puppets around above your head is exhausting work. “We meant to retire two years ago,” Jones laughs. “We wanted to concentrate on our annual festival in Cape Town. But then War Horse came along, and that has led to other offers. With shows like The Lion King and Avenue Q in the West End , puppets have become part of the mainstream theatre language.” Which must have been the last thing they expected when they started out in 1980. “Quite,” Kohler says. “I think we are all a little surprised that this 17th-century technology has such a new lease of life in the 21st century.”

The Return of Ulysses (Il ritorno d’Ulisse), King’s Theatre, Edinburgh (www.eft.co.uk 0131-473 2000), August 23 to 26