Mr. Burns (James Sugg, center) terrorizes the Simpson family with the help of Itchy and Scratchy in “Mr. Burns.”

When the world ends, the people who survive the plague/nuclear winter/supervolcano will still be telling stories. But which stories?

“The Simpsons” seemed like a good candidate for pop culture immortality, thought playwright Anne Washburn when she was brainstorming her new work. “Mr. Burns, a Post-Electric Play,” which runs through July 1 at Woolly Mammoth, opens on a group of people who have survived the fall of civilization (caused by a nuclear malfunction). They’re trying to remember an episode of “The Simpsons,” the one called “Cape Feare,” which was a send-up of a 1991 movie remake of a 1962 classic about a former convict who terrorizes a family.

“I just wanted to see what would happen with a pop culture narrative if you pushed it forward past the apocalypse,” says Washburn. Her characters try to recall the exact progression of the episode by reciting snippets of dialogue between its hero, Bart Simpson, and the evil Sideshow Bob. As the play moves seven years into the future, then 75, the retellings of “Cape Feare” transform from silly parody into a liturgical drama, with Mr. Burns (owner of the nuke plant in the Simpsons’ hometown of Springfield) morphing into the play-within-a-play’s villain — the embodiment of the dangers of nuclear power.

On the one hand, the episode that the survivors choose is anything but timeless — which actually exemplifies the main problem with “The Simpsons” as stand-alone culture: Every joke is a reference to something else. How can you find a parody funny if civilization has forgotten that the object of parody ever existed? On the other hand, its themes would resonate with a lost group of survivors terrified of being attacked by wild animals or hostile stragglers. “[It] is itself a story about people surviving outside of civilization,” says Washburn. “It’s a story about really deep, dark fears that they handle in a light and crazy way.

“I think ‘The Simpsons’ would have a good shot at survival,” she says. For one thing, it’s so quotable. “People tend to be fixated on the language of it. They tend to have memorized bits and pieces of it.”

The TV show is also populated with characters who represent enduring archetypes that have been around since mythology was invented. “Bart is the trickster, and in every culture that has legends or fables or stories, you have a trickster figure,” Washburn says.

“And Homer’s the fool — you always have a fool.”

Woolly Mammoth Theatre, 641 D St. NW; through July 1, $35-$77.50; 202-393-3939. (Archives)