In “Los Angeles,” the new play by Julian Sheppard now being staged by Adam Rapp at the Flea Theater’s tiny downstairs space, Katherine Waterston has a punishing assignment. She plays Audrey, who begins the play as a jittery depressive and gets emotionally pummeled in nearly every subsequent scene. It’s a setup so extreme that you might think the playwright a sadist and the actress — who spends much of the play with tears streaming down her face — a masochist.

Audrey’s story is a sordid, excruciating one. She moves to Los Angeles from Seattle with a boyfriend, who promptly dumps her. Already psychologically frail and seemingly unable to function in the world or even sustain a conversation, Audrey grows even more anxious as she finds herself alone in a cramped apartment in a strange, hostile city. Once she starts doing copious amounts of speed, she gets fired from her high-pressure Hollywood job. She then drags herself around in a state of painful anxiety, drugged and desperate for money.

Audrey’s pronounced neediness would send the entire world running in the opposite direction were it not for her sex appeal. Instead, in a series of two-person scenes where the actress is continually paired with a new character, she is used up and spit out by a series of grim acquaintances: a new female roommate who sizes up Audrey and offers “friendship” instead of rent; a coarse screenwriter who pays her for sex; an absentee father who refuses to say he loves her, and ultimately, a new boyfriend who uses the affection she so craves to control and manipulate her.

These scenes frequently end with Audrey shaking with sobs, her face a soggy mess, and — as if on cue — a small onstage rock band bursting into song, blaring tunes with odd lyrics like “Last night I accidentally ate my teeth.” These interludes disrupt but fail to illuminate — they mainly allow Ms. Waterston to change costumes onstage or grab a Kleenex en route to the next bruising encounter.

In its structure and writing, “Los Angeles” feels coltish, an early project of a writer with potential. Mr. Sheppard knows how to write naturalistic 20-something dialogue, but he can’t resist making forays into melodrama. His version of Los Angeles, a swirling hell filled with remorseless people who just want to use you to get ahead, is often convincing as a world. (Solid performances by the Bats, the Flea’s young resident company, certainly help.) And the director of “Los Angeles,” the wellregarded young playwright Mr. Rapp, draws the pain and ugliness out of the material, making his audience cringe each time Audrey is used and discarded. (He even stages some scenes on the railing separating the tiny audience from the stage — literally putting Audrey in the front row’s faces.)

Yet the production is not entirely sympathetic to the plight of a damaged woman trapped in a sexy body. There is a perceptible element of voyeurism here, an invitation to savor the exquisite tawdriness of Audrey’s saga. At times, the audience laughs when Audrey takes a drunken fall.

Mr. Rapp and his recent collaborators seem drawn to inconsequential stories of sexy young women under extreme duress — a questionable attraction. Last summer at the Rattlestick, Mr. Rapp directed Christopher Denham’s “Cagelove,” in which a pretty young woman who had been raped was then raped again — onstage — by her furious boyfriend. Shortly before, in his play “Red Light Winter” (at the Barrow Street Theater), an attractive young prostitute was used for sex by two best friends, developed HIV, and was roughly taken by one of them again (onstage).

Though Mr. Rapp has the skill to make these stories vivid, none of the three aforementioned productions has furnished a reason why the female character (and the audience) should go through so much anguish. There are times when “Los Angeles” seems to use its female protagonist much in the same way her acquaintances do. She’s easy on the eyes, she’s scantily dressed, and for the playwright and director, it seems to be fascinating and in some way artistically satisfying to watch her struggle to keep her head above water — the more frantic her struggle, the better. To this critic, however, it’s a form of theater that feels — for all its artsy trappings — like a cousin of sexism.

Until March 17 (41 White St., between Franklin Place and Church Street, 212-226-2407).