Most people consider the writer Sylvia Plath to have been a poet first (with the superlative Ariel), a novelist second (with the wrenching The Bell Jar), and that there her talents ended. The theatre director Robert Shaw begs to differ. His production of Plath's verse play, Three Women, has just opened in London - the second time it has been professionally staged. And Shaw believes the work shows Plath's brilliance as a dramatist."There is something magical about it that I have not tried to analyse too carefully," he says. "People respond to it and find things in this piece that they understand and relate to; things that perhaps Plath was able to express in a way no one else has."

Three Women is one of Plath's least-known - if not completely forgotten - pieces of writing. Originally written as a radio verse drama for three voices, it was broadcast in 1962 on the BBC Third Programme and later included in Winter Trees, a poetry collection first published in 1971 - eight years after Plath had killed herself, at the age of 30. Whether you call it a poem or a play, Three Women inspired the novelist Joyce Carol Oates to christen Plath "our acknowledged Queen of Sorrows, the spokeswoman for our most private, most helpless nightmares". And it is arguably one of her most beautiful pieces of writing.

With its themes of pregnancy, birth, miscarriage and adoption, it perfectly encapsulates the experience of becoming - or not becoming - a mother, including all the ecstasy and terror of childbirth. Shaw feels that Three Women was written specifically as a play. "When it was first broadcast, the characters did not have names," he says, "but they had descriptions. I don't want to get into the whole Ted Hughes-versus-Sylvia Plath thing but [to publish it as a poem] was clearly a decision that was taken after she was dead."

Plath's biographer, Peter K Steinberg, has suggested that this piece set the stage for her greatest work. "It's a shame [the play] hasn't received more focus - there's so much going on in it. All the themes come together in Three Women, and then she explodes into Ariel three months after completing it." Other Plath experts have suggested that this play deserves more analysis, as it marks the transition from her earlier poetry to the work she created at the height of her powers.

It took Shaw two years of negotiation with Plath's estate and her publisher, Faber & Faber, before he secured the rights to Three Women. Staging it is quite an undertaking: in Winter Trees it is clearly a poem and only 12 pages long; as a play it will run at about an hour long. But, says Shaw, its length belies its effect. "It has the power to reach out and touch people in a way that I find extraordinary."

Once he had embarked on his project, Shaw realised just how much attention Plath's name attracts. When he first put the word out about casting, he received 1,700 applications for the three female parts, and he eventually decided to cast three London actors in the roles. Elisabeth Dahl is First Voice, the woman who gives birth in hospital and takes her baby home. Tilly Fortune is Second Voice, a secretary who has a miscarriage (not her first). Lara Lemon is Third Voice, a student who has an unwanted pregnancy and gives her baby up for adoption.

Although Shaw is wary of seeing the piece as autobiographical, he describes Plath as having herself had a wide range of maternal experiences. She had given birth to her daughter Frieda in April 1960, had a miscarriage in February 1961 and had her son Nicholas in January 1962. Three Women was written in mid-1962 and broadcast in August. Plath killed herself in February 1963.

Both joyful and tragic, Three Women captures the beauty and weirdness of pregnancy. The "mother" character, First Voice, says in early pregnancy: "When I walk out, I am a great event ... I cannot help smiling at what it is I know." When her baby finally arrives, she is besotted: "What did my fingers do before they held him? What did my heart do, with its love? I have never seen a thing so clear." Meanwhile the Second Voice describes the everyday horror of miscarriage: "And the man I work for laughed: 'Have you seen something awful? You are so white, suddenly.' And I said nothing." The Third Voice sums up what it means to feel that you are not prepared for a baby: "I thought I could deny the consequence - but it was too late for that. It was too late, and the face went on shaping itself with love, as if I was ready."

Elisabeth Dahl's character gives birth during the course of the play - conveying Plath's description that "There is no miracle more cruel than this ... I am the centre of an atrocity." Dahl describes the play as Shakespearean. "It is so poetic that you can get lost in how beautiful it sounds and forget about the character. With an extreme situation like giving birth, it's almost like you couldn't use any other words, that you would have to be Sylvia Plath to put words to that. It is describing the indescribable." The ambivalence that her character feels about motherhood is striking. As Dahl explains, "There is one point when she starts to think there must be something wrong. Almost as if she is thinking: 'How can this be an innocent, normal baby when it's causing me so much pain? Maybe I'm giving birth to something evil.'" But, then, as Plath writes in Three Women: "The blue colour pales. He is human after all."

Lara Lemon plays the Third Voice, who gives up her baby. Although this is the one experience in the play that Plath had not lived through, Lemon feels that there are parallels with her other work: "Because my character is a student and we see her in hospital at the end, it really reminded me of some of the themes in The Bell Jar. We see her youth and her innocence slipping away."

The play is a powerful expression of pregnancy and maternity, but Shaw does not feel it is simply a "women's piece". "It has a kind of universality," he says. "She expresses someone's internal life in the most extraordinary way." How people will respond to the play, meanwhile, remains to be seen. "It is a risk," admits Shaw, "But it's an important risk to take. What we see is Plath the dramatist.

It gives us an idea of what we missed and what we might have had if we had had her for longer. Six months after it was broadcast, she died. It gives us a strong idea of what might have happened if she'd had a chance to develop it." He pauses. "It's really quite tantalising."

• Three Women is at the Jermyn Street Theatre, 16b Jermyn Street, London until 7 February. Box office: 020-7287 2875.

• This article was amended on Thursday 15 January 2009. The current production of Sylvia Plath's verse play, Three Women, at the Jermyn Street Theatre in London is not the first time the play has been professionally staged. The RSC performed it in 1974 in a production directed by Barry Kyle which later transferred to New York. This has been corrected.