Characters don’t come any vainer than the 55-year-old Frank Lloyd Wright in Richard Nelson’s new drama, “Frank’s Home.” To this white-haired gent in a light summer suit, the world and all its inhabitants — wife, mistress, children, friends, assistants — exist merely to fulfill his occasional desire for them. He seems constitutionally incapable of imagining how another person might feel.

A great man’s vanity — and its concomitant casualties — are the familiar themes trotted out in the rather predictable “Frank’s Home,” yet another drama about the high price of genius. As the title signals, Mr. Nelson’s muddled tale wants to be a family drama about the havoc Wright wreaked on his wife, mistress, children, friends, and colleagues. But the playwright can’t stop himself from drawing admiring portraits of the artist along the way. It’s these worshipful glimpses of the great man that leave the strongest impression.

From the famous architect’s first words — “Sometimes, I think I am America” — we know we’re in the presence of a megalomaniac. As embodied by Peter Weller, Wright is a dapper Peter Pan: He never wants to grow up, and he’s prone to outbursts and tantrums when anyone dares to interrupt his castle-building.

We meet him in 1923 on a dusty hill in Hollywood, where Wright, out of work and underappreciated, has come to build a progressive school. He stays in a nearby house with his entourage — his mistress, an assistant, and his old friend Louis Sullivan. And in a series of rather contrived garden-party scenes, Wright and crew are visited by his estranged adult children.

Brittle, querulous Catherine (Maggie Siff) still nourishes naïve hopes of being taken back into daddy’s arms, undeterred by decades of neglect. Her brother Lloyd (Jay Whittaker), an architect in his own right, is still seething from a failed attempt to work for his father.

Mr. Nelson attempts to superimpose the trappings of the dysfunctional family drama on the Wrights, but the framework doesn’t fit. Eruptions lead nowhere; catharsis is out of the question. And this version of Frank Lloyd Wright — cantankerous, self-righteous, domineering — is incapable of growing and changing.

Catherine and Lloyd may be enraged by the way their father openly mocks them, but they never storm out of a scene. They can’t shake the urge to be close to their famous, inaccessible father.

The audience, by contrast, has no inherent desire to linger in the presence of an egotistical tyrant. Especially when the playwright fails to provide reasons why we should care about his central character, and assumes the audience shares his boundless interest in Wright’s theories of architecture, his troubles with contractors, and his quest to build an earthquake-proof hotel.

Nor can we enter fully into the concerns of the other characters, since we only get to see them as victims. Pity for their circumstances soon gives way to frustration, as one after another, they take Wright’s abuse and come crawling back for more.

Only the estimable Harris Yulin, playing the architect Louis Sullivan, manages to bring his character fully to life. Sullivan, who’s come to California at Wright’s behest, is desperate for a job; with old age, his drawing hand has started to shake. Wright, with characteristic brutality, says he won’t give him one; he’s only brought him along for company. Sullivan reacts with anger, recrimination, and ultimately, humiliation. When he decides to stick around, it’s with bottle in hand and lump in throat.

To Wright, of course, Sullivan is another of the leech-like men who want a job from him. (His son, Lloyd, and his assistant are others.) While men harass him for jobs, women (including his hard-drinking mistress, his daughter, and even the local schoolteacher) press him for affection. He’s unwilling to give either.

Wright’s unremitting vanity feels barely plausible; it takes all Mr. Weller’s energy to animate his character. But ultimately it’s Robert Falls’s brisk direction that keeps the wooden dialogue and one-note characters from sinking into the torpor that lurks around the endless lawn-chair-bound scenes.

Mr. Falls propels “Frank’s Home” forward, but he can’t do much more than keep the marionettes bobbing on their strings. Mr. Nelson’s script hews close to the outline of the relevant facts, and often sounds cribbed from letters or diaries, but this isn’t a virtue. His characters come out starchy and stiff, locked into their historical slots. As they march along their predestined paths, all that emerges is a swirling cloud of surreal, all-devouring vanity.

Until February 18 (416 W. 42nd St. at Ninth Avenue, 212-279-4200).