Fans of “Cinderella” and “Peter Pan,” cover your ears and shield your eyes. Or don’t.

A troupe of Boston improv comedy veterans are taking the Disney tunes you know and love and morphing them into X-rated masterpieces, made up on the spot.

Dirty Disney’s raunchy send-ups have so far found a gleeful audience in the city, the show’s stars told Metro this week — even those who thought they knew what they were getting into.

“It’s funny. They come in with an expectation that the show is going to be dirty — it is what it is. And they’re still shocked every time we sing ‘The Circle of Life’ about a massive black dildo,” said cast member Patrick Parhiala. “It’s like, ‘No, this is what you wanted.’”

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The show works like this: audience members pick a gross or sexy prompt (venereal disease, sex positions), then a number at random that corresponds with a Disney tune. It’s the cast’s job to blend them together. A pianist supplies the live background music.

The results? Gems like “Got the Clap,” sung to the tune “Let it Go” from “Frozen,” or “We’re Having Sex Tonight,” sung to Randy Newman’s “Toy Story” classic “You’ve Got a Friend in Me.”

It’s the brainchild of Catalyst Comedy, the performers behind the made-up songs of the Boston Unscripted Musical Project. And it’s catching on. Both of Dirty Disney’s once-a-month shows so far have been sold out, and the cast said tickets are selling fast for performances booked through December at the cozy Boston Button Factory venue in Fort Point.

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Almost all the buzz so far has been through word of mouth, said co-founder Pablo Rojas.

He and his peers told Metro they believe the Dirty Disney ethos is so appealing because it taps into our desire to subvert the sacred and reject the restrained.

After all, said Rojas, people have been secretly consuming adult twists on pop culture — pervy cartoons and the like — for decades.

“It’s very clear the public wants this,” Rojas told Metro. “I think in general people are good and fun-loving and they like wholesome things, but when you tell them they can only do things in one specific way, there’s this reaction of: Really? Why?”

The show’s allure can also be traced back to pre-puberty, said co-founder and resident director Misch Whitaker, an established local improv comedian who also works as a nurse and studied human development.

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We all had sexual thoughts as kids, she told Metro, and it isn’t uncommon for children to have the hots for cartoons they grow up watching.

“I had a crush on [“The Little Mermaid” co-star] Prince Eric,” Whitaker said. “There’s a certain joy in going back to what you were attracted to in your childhood and then having fun with the idea of it.”

Dirty Disney returns Sept. 18 to the Button Factory at 50 Melcher Street. Tickets are $10.

Stay tuned. Founders told Metro the show’s success has them considering moving the show to a bigger venue in the city, or adding more performances to their calendar.