LIKE a clumsy kid in the schoolyard Shakespeare’s late play “Cymbeline” has suffered plenty of bullying. George Bernard Shaw called it “exasperating beyond all tolerance.” Henry James named it “a florid fairy tale.” And Samuel Johnson, its chief tormenter, said that to discuss the play “were to waste criticism upon unresisting imbecility, upon faults too evident for detection, and too gross for aggravation.”

Even the script itself seems aware of its absurdities: its banishments, beheadings, kidnappings, wars and reunions. In the opening scene a courtier vainly assures the audience that this play, “may well be laughed at,/Yet is it true.” Hardly. The tender strangeness of other Shakespeare plays — Hamlet’s sea voyage, the animate statue in “The Winter’s Tale” — must yield to “Cymbeline’s” final act, which discloses more than two dozen improbable secrets with machine-gun speed.

Despite these flaws — and maybe because of them — Fiasco Theater, a plucky New York sextet, can’t resist the play. In the past two years Fiasco has staged three runs of “Cymbeline” and has resuscitated it again at Barrow Street Theater in the West Village, where it is in previews and is set to open Thursday.

Fiasco’s success is, like “Cymbeline,” something of a fairy tale. Sitting in a sunlit Times Square rehearsal space where the company was readying the show for its new engagement, Ben Steinfeld, a company member, said: “Our story is preposterous. It’s hard to believe.” Yet it is true.