The only thing that catches fire in Arena Stage's disappointing "Anna in the Tropics," the story of a family of cigar makers in sultry, Depression-era Tampa, is the tobacco.

Nilo Cruz's 2002 play has had a privileged childhood: a Pulitzer Prize, a star-powered Broadway production, mountings at highly regarded regional theaters across the country. Such a glittering rollout suggests a work of more than embryonic promise. But what director Jo Bonney presents on the stage of the Kreeger Theater is a surprisingly static piece of drama, one that fails to instill even a scintilla of urgency in the combustible relationships it recounts.

Prettiness here is an affliction. The factory in which the Cuban immigrant family stuffs and wraps its cigars is oddly immaculate, and so is Cruz's poetry. The people of "Anna in the Tropics" speak in exquisite-sounding allusions, and no one more reliably than Marela (Michele Vazquez), "Anna's" ingenue, who is given to dewy declarations like "A bicycle dreams of being a boy." The more burdensome freight on the play's literary manifest has to do with the interweaving of themes from Tolstoy's "Anna Karenina," which figures heavily in the plot; the novel is narrated daily in the factory by a "lector" (Jason Manuel Olazabal), who has been hired to read stories to the illiterate workers.

You'd think that all these bookish conceits would lend the piece an air of intense cerebration, but the schematic "Anna in the Tropics" actually plays as if it has not been rigorously worked out. This is especially the case after intermission, when the dramatist makes a disastrous foray into melodrama, resorting improbably to a rape and some gunfire to invigorate the play's resolution. The report of a pistol may have been a stunning stage effect in the time of Ibsen and Chekhov; in 21st-century theater, however, gunpowder smells a lot like desperation.

Cruz's subject and setting certainly provide rich material for atmospheric drama, in the style of Chekhov. It is 1929 in Ybor City, a section of Tampa where many Cubans have come to live and work, and where the traditions of their native island do not always mesh with their polyglot adoptive culture. The cigar factory owned by Santiago (Mateo Gomez) and his brother Cheche (Chaz Mena) is a petri dish for the clash of values: Santiago and his wife, Ofelia (Marian Licha), are advocates of the old, elegant way of doing business, including the employment of the urbane lector; Cheche is equally set on change, on sweeping out antique methods and importing the tools of the more modern society they've joined.

The shopworn roles of men and women are also under attack in "Anna in the Tropics." Santiago and Ofelia's older daughter, Conchita (Yetta Gottesman), bristles at the inequity in her marriage to Palomo (Felix Solis); she yearns for the freedom to look for love outside her marriage, as Palomo has done. It is Olazabal's dapper lector who is the flash point in both the romantic and economic themes of the story, and it comes as no great shock to learn which of the characters is the victim of the crushing blows that jealousy and modernity can deliver.

Cruz's gift is the decorous turn of phrase; language is what seems to interest him, and as a result his characters are all artfully articulate. You can see, too, why the notion of a dreary world of piecework immeasurably uplifted by the words of Tolstoy or Dickens would tickle his fancy. While he's able to write his way into the heart of a miserably unfulfilled wife, however, he struggles to write himself out of a scene, and so time after time in "Anna in the Tropics," a dramatic situation tends to drift off in wispy clouds. We're dragged, rather than propelled, through events, and the result is an evening that slogs along to an uncertain conclusion.

Bonney doesn't add sinew or muscle to Cruz's character-driven narrative, and the production is not deeply evocative. Set designer Loy Arcenas does a serviceable job of taking us inside the factory, conjuring a dark interior of brick and timber, and Ilona Somogyi's costumes are handsome and bland. The snippets of music between scenes, in fact, are the liveliest indication of the time and the place to which "Anna" is supposed to take us.

The actors all succeed in the essential task of seeming of the period; in some cases, however, they're confronted with characters whose identities do not evolve in stimulating ways. Licha's Ofelia, for instance, has a big part and is a warm creation, but also evinces little vital function in the story. Possessed of the most nuanced of the roles, Solis and Gottesman also offer the most incisive portrayals. Gottesman, in particular, gives a voluptuous credibility to a woman in search of a more potent way of satisfying a need for attention and affection.

That's all the slow burn that this "Anna" has to offer, unfortunately. The rest is just slow.

Anna in the Tropics, by Nilo Cruz. Directed by Jo Bonney. Set, Loy Arcenas; costumes, Ilona Somogyi; lighting, Scott Zielinski; sound, Darron L. West; speech consultant, Kim Bey. Approximately 2 hours 10 minutes. Through Nov. 21 at Arena Stage, 1101 Sixth St. SW. Call 202-488-3300 or visit www.arenastage.org.

From left, Mateo Gomez, Yetta Gottesman, Michele Vazquez and Felix Solis.