THE remains of a dinner party are neatly stacked along the side of Rehearsal Room 2, deep under the National Theatre. Mark Rylance looks fresh enough after a day spent as Henri in Yasmina Reza's latest play, Life x 3, but he isn't quite ready to leave and, next to the trays of wine glasses and crumbs, he dons a pair of shorts, long red woolly socks and a wind-cheater. He intends to cycle home to Herne Hill in south London. Despite the lingering up-market heart-throb image, he isn't much concerned with glamour.

Free spirit: after five years, Mark Rylance is relieved to be working on a different stage from the Globe's - but he still loves the replica theatre

Now 40, he has completed five successful years as artistic director of Shakespeare's Globe. More than 250,000 people bought tickets for the 2000 season, during which he played Hamlet, to great acclaim, for the second time. He is the first actor to attempt the part in an environment like the one that Richard Burbage knew when he uttered Shakespeare's newly written lines.

He is planning next season and contemplating another possible three years in charge at the Globe, but for the next few months he will be here, at the National. Delicate-featured, boyish despite thinning hair, he talks earnestly and freely. The throaty chuckle that he uses to such effect on stage is not much in evidence.

He is, first and foremost, an actor, isn't he? Has embracing managerial responsibility curtailed his performing opportunities?

"No, not at all," he says. "The opportunity to act at the Globe is more thrilling than the opportunity to act anywhere else. And to be in at the birth of a new theatre - and in a building like the Globe!"

He has taken every possible challenge on the replica Elizabethan stage, playing a touching Henry V and a flirtatious Cleopatra as well as Hamlet and small comic parts. But during his tenure at the Globe, he hasn't spent a long period at another theatre.

"It's the first year I've felt it possible to go away. Peter Kyle [the general manager, appointed two years ago] has put structures in place which are liberating for me. It's rather nice to be in another theatre - especially one I'm not responsible for."

He felt sufficiently free to take a break earlier in the year as well, to play the lead role in Intimacy, a film directed by Patrice Chereau based on a couple of Hanif Kureishi's stories. "It's about sensual, physical intimacy as opposed to knowing about someone," he says. Intimacy is due to be released next year.

The National's schedules have been adjusted to enable him to be in Life x 3, working with an old friend. Matthew Warchus directed him as a charming, Ulster-toned, diminutive Benedick to Janet McTeer's willowy Beatrice in Much Ado About Nothing in the West End in 1994 and in True West by Sam Shepard at the Donmar Warehouse. They have wanted to work together again for some time.

Yasmina Reza's new play requires a feat of memory - the script is performed three times with subtle differences, the "x 3" of the title. Rylance plays an ambitious astrophysicist, Henri, attempting to publish a paper on "the flattening of galaxy haloes". Is it about parallel universes, the ripple effect of the tiniest action, or playing with ideas of time?

"I think," says Rylance enigmatically, "audiences will enjoy exploring all those ideas."

Henri and his wife (played by Harriet Walter) host a disastrous dinner party when the guests (Imelda Staunton and Oliver Cotton, playing a rival scientist) arrive a day early. During their researches, Rylance and Cotton visited Imperial College to learn from some real astrophysicists.

"When you get your head round the distance, the size of the universe, as the scientists said to us, it absolutely changes your perspective about life and you do feel separate from people in the street," says Rylance. "Considering the heavens is very imaginative. But it's a career too, and it's competitive.

"You certainly don't need to understand science to enjoy the play. It's very straightforward really, but it has the quality of modern dance. It's about gravity, a galaxy of four planets or four people, the loosening or tightening of the pull, the expanding and contracting between them."

It is no surprise that the mind-stretching concepts of astrophysics appeal to Rylance, who has sometimes been accused of espousing eccentric ideas. He is a believer in ley lines and the power of dreams and, despite being artistic director of Shakespeare's Globe, he says that he's not altogether sure that "the Stratford man" wrote the plays (he advocates Francis Bacon, but enjoys the mystery of not knowing for sure).

When off-duty, he takes part with Richard Olivier (director son of Laurence) in an organisation called Wild Dance, a kind of male empowerment group like those formed in America in the wake of feminism. It attracts men from all backgrounds to share stories, poetry, inspiration. "It was a kind of admission that men were finding it difficult to deliver what is expected of them: justice, leadership, not resorting to violence." He describes his interests straightforwardly but cautiously, knowing that they might attract mockery.

After a couple of hours, the Rylance pager goes off. His wife of more than a decade, the composer Claire van Kampen, is pleased to say that she has completed her latest score. He whoops with delight. The couple met here at the National in 1987, when they were both involved in Mike Alfreds's production of The Wandering Jew. Rylance mentions that he has been along to take a peep into the rehearsal room where they first saw each other.

It seems that Mark Rylance - actor, theatre manager, mystical thinker - is also an inveterate romantic.