Marc Quinn is best known for his blood sculptures. Now, with a new show at IMMA, he is moving on to meat, he tells Aidan Dunne

The sculptor Marc Quinn is best known for Self, his iconic self-portrait made from nine pints of his own blood, a startling piece of work that is now one of the cornerstones of the Saatchi collection.

Accumulated, naturally enough, over a period of months, the blood was poured into a mould taken from life and frozen. It is permanently refrigerated, otherwise it would melt, and its precarious status invites reflections on mortality, transience and the fragility of life. It is also an ambiguously enticing object, strangely beautiful but, once we know what exactly it is, almost repellent. That mixture of the real, the aesthetic and the disturbing is typical of his work.

There is another piece that might come to rival Self as a signature piece: his sculptural portrait of Alison Lapper, originally cast from life and then carved in marble. The statue of Lapper, who was born without arms and with attenuated legs, is one of a series of comparable marble pieces. Next year a four-metre-high version of the sculpture will occupy one of the plinths in Trafalgar Square, in London, for 12 months. A contemporary Venus de Milo, with its provocative allusion to classical statuary, it challenges our preconceptions about beauty and completeness and has already provoked controversy and some lively debate.

Quinn's first solo show in Ireland has just opened at the Irish Museum of Modern Art. Flesh consists of a new series of works not previously exhibited. They are all black-patinated bronzes, varied in scale and all cast from animal carcasses, including a bull, stags, sheep and rabbits.

Brutally truncated, each looks very much as if it is the product of the slaughterhouse, and it is. All of them are taken from the meat-industry chain, from meat markets and wholesalers, so what we are looking at is basically meat.

But the torsos are also carefully arranged in attitudes that recall classical figurative sculpture, something underlined by the descriptive titles: Reclining Figure (Lamb) or Torso (Stag). And at first glance they look disconcertingly like figurative sculptures, albeit sculptures in which something has gone oddly awry. They compel and disturb. As Quinn remarks with a wry smile: "Francis Bacon meets Henry Moore."

For someone whose work often delves into dark areas he is surprisingly cheerful and easy-going in person. Thoughtful and reserved, he answers questions carefully and precisely. He wanted them, he says, to come across as Rodinesque figures. "In a way the whole black polished look is a way of distracting you from what they are. It tricks you about what you're looking at. I also had it in mind that the patina is bound up with the whole idea of civilisation, of civilised values, but it's only the thinnest veneer, and civilisation can only exist because other things perish all the time to maintain it."

The bronzes are extraordinary presences, heroic and tragic, touching and absurd. As Darian Leader writes in his catalogue essay, they "all seem to want something from us". It is odd how easily we read them as being human, but it is as if, in Leader's formulation, "through sculpting something that is not the human body, he has sculpted the human body. In fact, the human body is so reduced to its essentials that we could even call these works minimal".

It's not that Quinn is implying that these animals are like us; he is implying that we see ourselves in them, which is rather a different and infinitely less reassuring proposition. Furthermore, as we have become accustomed in recent years to a daily diet of images of atrocities and mayhem of various kinds, from Omagh to Bosnia, Jerusalem to Baghdad, it is all the easier, uncomfortably easier, to see that.

The critically injured Snowden's secret, Yossarian discovers in Joseph Heller's novel Catch-22, is that man is meat.

It's a visceral message that has understandably fascinated many artists. Quinn's work usually engages with artistic tradition, and Flesh is no exception. One thinks of Rembrandt's celebrated painting of a slaughtered ox, or of Chaim Soutine's series of paintings of meat, or of Francis Bacon's incorporation of meat in a crucifixion study. In Ireland Barrie Cooke made a memorable series of animal-carcass paintings in the 1960s, and Camille Souter made paintings in a slaughterhouse in the 1970s. Quinn's YBA contemporary Damien Hirst has famously used preserved animals carcasses in several works.

Quinn likes the idea that he is revisiting a classical theme and doing so in terms of classical technique. There is certainly something of the baroque about the way the flesh pulls away from bone in beautiful, rippling folds, like drapery, and a wealth of sensual detail in the fine-grained surfaces.

"There's nothing in these sculptures that couldn't have been done in Rembrandt's time. The sculptural techniques are old, it's just that I've used them to make a new image. So it's a question of sensibility. It occurs to us now to look at things in this way."

And it's true that one can readily imagine his bronzes in the context of an exhibition of European figurative sculpture. They logically belong, and they add something: they provide an enhancement, an additional perspective.

"A hundred years ago they would have been looked at in an entirely different way," he says. "Before that we were pretty secure in our position at the top of the food chain. Animals had been put there for our use. That certainty has gone."

But it has been replaced by other kinds of complacency. Although these images of truncated, eviscerated animals are inevitably shocking, they wouldn't, I suggest, shock farmers, butchers or people who hunt and fish. "No, they wouldn't," Quinn agrees. "I live in London, and meat is neatly packaged or beautifully cooked and served in restaurants. In a way these are sculptures for people who live in London or in other cities, people who never see animals and are abstracted from the reality of nature. But that's more and more people now. It's easy to forget that we humans are animals ourselves."

Leader makes the point that we habitually encounter meat as fragmented and separated rather than as a whole, large animal. Quinn agrees. "Food is seductive. You order calf's liver in a restaurant and something beautiful and enticing arrives. That last thing on your mind is that it's part of an animal. We don't want to be reminded of that."

There is a moral issue here, but, as Quinn points out, he eats meat himself, and the sculptures are not intended to be moralistic. "I'm just pointing out that this is the way it is. Really, they are about accepting where we are."

• Flesh is at the Irish Museum of Modern Art, Dublin, until September 12th