Elaine Cassidy at the Donmar: take control and cut the chit-chat

"Oh, Anna," sighs Elaine Cassidy. "She really saddens me." The Irish actor feels for her character in Brian Friel's poignant adaptation of Fathers and Sons, Ivan Turgenev's 1862 novel, now on at the Donmar Warehouse, London.

Anna Odintsova is a young widow holding tight to her feelings; Cassidy, talking up a storm, doesn't hold back. Her eyes shine like small dark stones – perfect for those roles of secrets and sorrows in which she's often cast. In cinema, she's starred in Felicia's Journey and Disco Pigs; on television more recently she was an heiress in The Paradise, the BBC's version of Zola transplanted to northern England.

Turgenev's reputation has been overshadowed by his younger contemporary Chekhov, but he is an enthralling, lyrical writer. Friel describes him as "a ditherer, racked between irreconcilable beliefs and compulsions": he adored Russia but mostly lived abroad, and adored the singer Pauline Viardot, yet was hardly faithful. He was, Friel says, "always haunted by a sense that real life, a life of content and fulfilment, had somehow eluded him but was available elsewhere".

That sense that life happens somewhere else – another time, another place – pervades Fathers and Sons. Those sons – brilliant Yevgeny Bazarov and his pal Kirsanov Arkady – return from university determined to overturn sclerotic Russia. Their fathers are cowed by these clever children. Anna's arrival proves a catalyst to the young men. Turgenev, like Friel, extends heartfelt sympathies to all his conflicted, yearning characters.

Looking out for a younger sister and batty aunt, Anna keeps her head screwed on, despite a troubled backstory that could supply a play in itself. "Anna gave up so much for survival, but it's never felt like she harboured resentment," Cassidy says. "It's lovely to play a character who's so rich."

That richness includes financial nous; you rarely see a period heroine formulating a business plan, but Anna helps Kirsanov's hapless father order his estate. Cassidy recites her credo. "Routine. Order. Discipline. She is the Hotel Inspector!" But no spreadsheet can ward off misery – Anna responds guardedly to Yevgeny's vehement declarations but feels deeply for him. "The life she could have had!" Cassidy laments. "I hope I never experience that regret."

Cassidy tells me that these rehearsals are unusually devoted to research and discussion. "I've played characters from a similar period," she says, "but Russian women had a little bit more freedom. They had control of their own dowry through the marriage. That was quite liberating, even if they couldn't get divorced." An ensemble that includes Broadway's Seth Numrich, last seen in London in Sweet Bird of Youth at the Old Vic, has located their inner Russian. "We found that the Russians really wouldn't do chit-chat," Cassidy says.

Friel, now 85, is a longtime hero of Cassidy's. She met him at the beginning of her career, unsuccessfully auditioning at the Abbey in Dublin. His Fathers and Sons script reads like a dream and was originally presented by the National Theatre in 1987 (Ralph Fiennes played Arkady). The Old Vic staged Turgenev's Fortune's Fool last winter, but A Month in the Country is his only play with a foothold in the repertoire. (Friel has also translated that play.) Initially poorly received, A Month in the Country found new favour in the wake of Chekhov's success when, as Friel puts it, "the undramatic became the new drama".

This powerfully subdued undertow characterises Friel's own plays, as director Lyndsey Turner proved with Philadelphia, Here I Come! at the Donmar. Turner has since won an Olivier award for Chimerica; Cassidy, who met her at a workshop at the Royal Court, jumped at another opportunity to work with her. What makes Turner special? "She's a grafter," Cassidy says. "She expects hard work because she works harder than any of us. She's so clever – her instincts are always bang on. She's the real deal."

Early in her career, Cassidy caught the eye of world-class directors. "I've hit the jackpot," she admits. Peter Gill directed Scenes from the Big Picture at the National Theatre. "To me he was a genius, and I don't use that word lightly. The twinkle inside him! We were the young ones, so he nurtured us." On screen, Atom Egoyan cast her opposite Bob Hoskins in Felicia's Journey. Hoskins' death reconnected them recently: she says Egoyan "hasn't changed at all – he's still an excited kid in a sweetshop".

Cassidy, pouncing on a round Russian cookie, is pretty excited herself, but admits to some trepidation about the audience's proximity in the intimate Donmar. "The first time I got that feeling of seeing knees was at the Almeida," she recalls. At the first preview of There Came a Gypsy Riding, "I got stage fright – everything was going blotched." Autopiloting through a scene with Eileen Atkins and looking for an escape route, she finally told herself: "Elaine, cop yourself on and get on with it." Afterwards, my husband said, 'You looked so relaxed.' I said, 'I was dying! I nearly fainted.' I hate fear, and I just did not want it to get the better of me."

"What a weird job we do," she says. "You put your body through such trauma – you know you're in a play but your body doesn't." In 2006, she played Abigail Williams, whose accusations spark a witchhunt in Arthur Miller's The Crucible. "All us Salem girls had a breakdown through the run, for different reasons," she says. "I had my breakdown on stage, at the very end of the run." When Iain Glen, as Abigail's furious victim, grabbed her hair, it all got too much and she stood sobbing onstage. "I used to have spasms in my body, playing Abigail. It was a dark place, but it was worth it – I handed over my life to her."

As she returns to rehearsals, she says, "I still feel that we're at the beginning of the journey. But it's a well-made house, an old house, not a new build. It's sturdy. The foundations are strong."