In his new drama, “Lower Ninth,” now at the Flea, the young playwright Beau Willimon takes on that formidable behemoth, Hurricane Katrina. Mr. Willimon is a smart, deft writer on the rise; his political yarn “Farragut North,” Broadway-bound, has generated considerable advance buzz. But despite his gifts, he can’t quite wrestle the overwhelming horror of Katrina into the quiet form of the three-character stage play.

“Lower Ninth” takes place in the midst of the flood, on an asphalt-shingled rooftop in New Orleans’s poverty-stricken Lower Ninth Ward. Three African-American men are stranded there, wondering if someone will show up to rescue them before they die. The sun beats down on them. They have no food, no water. And one of them, Lowboy (Gbenga Akinnagbe), is already dead, his corpse covered with a trash bag.

Lowboy, we learn, was a brash young gang leader, the kind of guy who always thought he would die from a bullet in his head. The younger E-Z (Gaius Charles), who looked up to Lowboy but lacks his cool instinct for guns, dragged Lowboy’s body up onto the roof. He passes the monotonous, terrifying hours with Malcolm (James McDaniel), whose lined face and shuffling step suggest a long history of survival.

The three men are representatives of a population that was suffering long before Katrina hit, and Mr. Willimon draws them according to type. Drug dealer Lowboy (who speaks to E-Z in a long dream) is arrogant but smart, a self-made man with the warped ethics of a Mob boss. Good kid E-Z is lost and unsure of himself, grasping for options that never come. Wise old Malcolm is an addict-turned-preacher, a still-broken man who can barely acknowledge the fact that E-Z is his (much-neglected) son. We have seen these characters — and their conflicts — before, and though “Lower Ninth” draws them adeptly, they feel familiar. It’s in the characters’ moments of humor or pragmatism that the writing feels fresh. When E-Z and Malcolm play “20 Questions” on the rooftop, squabbling over the rules, the play comes alive. It’s as if the naturalistic mode is the only one in which the magnitude of Katrina can be absorbed.

Likewise, the director, Daniel Goldstein, does his best work when he’s not striking solemn notes. Most effective of all are the times when he gets familiar banter going between his talented actors. As Lowboy, the charismatic Mr. Akinnagbe is compulsively watchable. And playing the reluctant father and son, Messrs. McDaniel and Charles have an honest, convincing rapport.

But when Mr. Willimon attempts to cloak these Everymen in metaphor and myth, “Lower Ninth” falls flat. The insertion of Bible stories and discussions of faith feels heavy-handed, and lines such as “You could have saved him before the storm” sound like cues for a commercial break. The mournful trumpet solos that serve as transitions between scenes remind us again and again, This Is A Tragedy.

No one could dispute that point. Strangely, though, “Lower Ninth” feels phony when it’s served up as tragedy. The more Mr. Willimon tries to make his tale an epic, the more it resists that stature. Though the play layers a lot of biography and metaphor over the basic predicament of two men stranded on a roof, there is nothing in “Lower Ninth” nearly as compelling as those two men stranded on a roof. As those indelible images from the nightly news reminded us again and again, the narrative of Katrina was the narrative of survival.

Until April 5 (41 White St., between Broadway and Church Street, 212-226-2407).