Think of the most troubled women in theatre and Medea comes pretty high on the list. A byword for narcissism and violence, she is abandoned by her husband, and lashes out by killing their children. Yet to hear Rachael Stirling talk about the character she is about to play, you'd think Medea was a role model for the smart, modern woman.

"I really enjoy and embrace her," says Stirling. "Normally, the central character on stage, the wittiest, funniest, cleverest character, is the male: the woman is the foil. But Medea is the one who's far more intuitive, far more insightful, far more funny. I love her brashness – I'm slightly vulgar in life and I like her vulgarity, it makes me laugh. I admire her: obviously the course of action she takes is extreme, but I like the fact that she doesn't accept that her husband runs off, as society expects of her. I love her strength of will, her pragmatism." There's more, but you get the idea.

You could put Stirling's enthusiasm down to the fact that she's playing Medea in a new version written and directed by Mike Bartlett (who wrote the acclaimed Cock, and whose adaptation of Chariots of Fire is now in the West End). Bartlett has shifted the action from ancient Greece to a British new-build housing estate, and shaped the character around his lead actor, isolating Medea from her community by emphasising Stirling's strong RP accent, in sharp contrast to the estuary tones of the suburbanites around her.

If the role is one of theatre's most challenging, it is striking how many actors recall playing Medea with real passion. Fiona Shaw, who took the role in Dublin, London and New York between 2000 and 2003, thinks it is because Euripides, the Greek playwright who shaped her for the stage in 431BC, expertly manipulated his audiences' emotions. "He's absolutely meticulous about cornering her," Shaw says. Minutes into the first act, we learn that Medea has already defied her father, executed her brother, and abandoned her home, all for the love of her husband, Jason – which amplifies her sense of betrayal when Jason decides to secure his political future by marrying a king's daughter. In this situation, says Shaw, "there is absolutely nowhere for her to go. That is brilliantly, mathematically set up. Thereafter, the audience feel sympathetic, right until the moment when she says: 'I must kill the children.' It's not surprising she's infamous for killing them – but we should be infamous for agreeing to it."

Far from being a willing infanticide, Shaw argues, Medea forces herself to kill her children so that no one else can. It is, like everything else she does, an act of selfishness driven by sexual passion. "What she's really on to is the terrible myth in our society, whereby we tell children that they are the primary source of love, and the cruel truth is that they're not: the passionate partner is. People will not give up their lover for their children."

Maureen Beattie, who took the role in a landmark Scottish production in 2000, loves Medea's vitality. "She gets you into the palm of her hand. She makes you laugh, she makes you cry with her. And she makes terrible fun of Jason. She's like a boxer in a fairground: you can pay five dollars to go in and do a round with her, and she just sees everyone off." Nina Kristofferson, who played Medea for Northern Broadsides two years ago, puts it more simply: "Medea is one of the best roles you can play. There are so many layers, such a depth of emotion to bring out."

Every actor I speak to who has played Medea talks about a heightened awareness of news stories about parents – men and women – killing their children in similar circumstances. The fury and wounded pride the character experiences at being rejected for a younger woman give Medea a kind of normalcy. Beattie still recalls the first line spoken to her by Jason, in Liz Lochhead's adaptation: "'It's not what you think.' That's just a stormer. I don't think there's a woman I know who hasn't had that one."

For Stirling, Medea was close to the bone for different reasons. As a teenager, she watched the play "maybe half a dozen times", when her mother, Diana Rigg, played Medea in a 1992 production, which transferred to the West End and then Broadway, where Rigg won a Tony award. Stirling is reluctant to talk about her mother, keen to emphasise that she is her own person. But as a 15-year-old, she says, Medea "made total sense to me". Her parents had divorced in 1990, a split prompted by Archibald Stirling's affair with Joely Richardson, 27 years Rigg's junior. "I had a very keen experience of what happens when a family breaks up for exactly the same reason as happens in the play," says Stirling. "I understood."

A rewarding role, it is also difficult and draining. "I didn't want to do the play at all," admits Shaw. "I don't want to be doing plays that are conjuring badness, because they make you feel full of badness. Not the desire to kill children, just full of the desire to be depressed. And I did get very depressed." Beattie felt utterly exhausted after each performance: "I would sleep right through for 11 hours."

Tanya Moodie, who played Medea at the West Yorkshire Playhouse in 2003, had an even more disturbing experience. "I felt I was working in a haunted house," she says. "Odd things would happen. I had a lot of physical injuries. When I was working on Medea in my flat, the radio would turn on by itself." Weirder still, she began to apprehend Medea as a kind of possessing spirit: "She would start to try to inhabit me before I even got to the theatre. That had never happened before, and it's never happened again."

It feels fitting that someone should have had a supernatural experience: in Greek myth and Euripides' play, Medea is the granddaughter of the sun-god Helios and niece of Circe, a witch. Bartlett has retained an element of magic in his updated version: Stirling says they have worked together to make this as believable as possible. "She likes disconcerting the people around her," explains Stirling. "She knows she frightens people, and draws on the mystical to unsettle them."

Even in the more traditional productions, Medea's godly lineage is problematic, because Euripides uses it to avoid the question of guilt. "How do you cope with playing somebody as dark as that, when she's so relentlessly not guilty?" asks Beattie. In the original play, Medea leaves the killing scene in triumph, rising to the heavens in a golden chariot. Kristofferson refuses to read this as pure victory: "We cannot get away from our own minds. Kill your own, and part of you will no longer live." Shaw and her director, Deborah Warner, decided to do away with the gods and the chariot altogether: instead, Shaw's Medea ended the play flirtatiously flicking water in Jason's face. "Somehow," she says, "you felt the whole thing was going to happen again."