Thousands of people at the Burning Man festival, an annual carefree celebration of art, music and counterculture vibes in a remote patch of Nevada desert, remained stranded there Sunday after torrential rains turned roads and grounds into muck, cutting off access.

It was an unusual turn of events that tested the resolve of participants, who were told to conserve food and water, at the more than three-decade-old festival that prides itself on grit and self-reliance and normally battles excessive heat and, sometimes, excessive partying.

True to form, some took it in stride.

“Burning Man is an all-weather state of mind,” said Star Heartsong, 43, a tech entrepreneur who came from Austin, Texas. He added that “when it’s time to leave, we’ll leave.”

“Burners aren’t victims,” he said, using the name that attendees are known by.

But the authorities were investigating the death of one participant, and the worsening conditions on Sunday — it was raining harder in the afternoon than on the previous two days — could delay people leaving the event, which ends Monday and in normal conditions causes a lengthy traffic backup.

Accounts of the mud and efforts to leave ricocheted across social media and became something of a sensation in itself.

In a video posted by the music producer Diplo on Saturday evening on X, formerly known as Twitter, he can be seen leaving the festival with the comedian Chris Rock and others on the back of a vehicle. “just walked 5 miles in the mud out of burning man with chris rock and a fan picked us up,” Diplo wrote.

Neal Katyal, a law professor at Georgetown University and former acting solicitor general in the Obama administration, said that he and several others hiked six miles to Gerlach, Nev., the nearest town.

Mr. Katyal and his group filled their backpacks with the essentials: “flashlights, water, extra socks — some of us like me had to bring our computers,” he said. They put plastic bags on their bare feet, socks over the top of them, and then put their boots or shoes on to “avoid being soaked,” he said.

“The hike was quite hard,” Mr. Katyal said, adding that the mud was “extremely sticky and heavy” and some people in the group almost fell. He expressed concern for those still looking to depart. “I think it is going to be very hard for people to leave for some days, but I think so many of the folks there have such a good spirit, dancing and making the most of it,” he said.

The festival — which culminates in, and takes its name from, the burning of a giant sculpture of a man, now scheduled for Sunday night — is held in Black Rock City, a temporary community that pops up each year in the middle of the Black Rock Desert in northwestern Nevada, a vast space known during the event as “the playa.”

Since 1986, when a small group of artists and friends gathered on Baker Beach in San Francisco to celebrate the summer solstice by burning a wooden figure of a man, Burning Man has been a magnet for artists, bohemians, tech workers, celebrities, social media influencers, and people seeking a fun Labor Day activity and ready to practice the festival’s core ethic of “radical self-reliance.”

The makeshift town hosts more than 70,000 people every year and is a three-hour drive from the nearest airport, which is more than 100 miles away in Reno. This year’s event began on Aug. 27.

Heavy rains began on Friday, and the festival site received more than half an inch of rain overnight, organizers said.

In other areas of Nevada, such as Las Vegas, fast-moving thunderstorms and flash flooding swept through over the weekend, with heavy flooding reported on the Las Vegas Strip. At least one driver had to be rescued from a car.

The rains on Saturday flooded many campsites at the festival and led organizers to urge attendees to shelter in place and conserve food and water.

On Sunday, after a mostly dry night, the morning skies were partly sunny. Many camps took advantage of the dry lull to dismantle nonessential structures — living room tents, dance spaces and bars — and prepare for a faster exit when the playa road became drivable.

In the afternoon, heavy rain fell again. No driving was permitted on the festival grounds except for emergency services. Some vehicles with four-wheel drive and all-terrain tires had been able to navigate the mud and leave, but others, including dozens of R.V.s and Jeeps, tried and got stuck.

Festival organizers said there was a chance that late on Monday it would be possible to leave in vehicles and R.V.s, but only if conditions allow. Organizers also said that they would have buses in Gerlach to drive people to Reno.

The eventual departure of tens of thousands of people could be a nightmare, considering the condition of the roads and that traffic backups of more than 12 hours were typical in past years.

“I cried already,” said Carla Ferreira, 33, a real estate developer from Las Vegas. “I’m overwhelmed that there are 73,000 people who need to leave safely. We might have to wait until Tuesday.”

Still, the flooding, the mud and the confinement have not disrupted the party for many of the 70,000-plus burners. They have kept dancing to ever-present, bass-heavy house music blasting across the desert; doing yoga; and visiting one another’s camps to drink and socialize and discuss the popular topic of how to make Burning Man better.

On Saturday afternoon, in the Playa Piano Bar, the musician Eric Lewis, known as ELEW, 51, belted out a marathon three-hour set of jazz and rock under an open-sided tent. Outside, water lay in puddles. Inside, he was surrounded by two dozen burners dressed in G-strings and Jedi garb. But their feet were bare or in plastic bags, instead of platform shoes and boots.

One attendee, Angie Peacock, 44, said in a phone interview that though there was some anxiety among the people and the weather temporarily halted some partying, the spirit of the festival was still on display on Saturday night. Earlier, one of the campers said that they had enough food and provisions to last at least 10 days.

“We’re not going to let anyone starve, you know?” Ms. Peacock said. “This is not ‘Hunger Games.’”

On Saturday night, neon lights were still visible across the makeshift city, and the raves were continuing as usual.

“It’s lit up,” Ms. Peacock said, looking out. “It’s beautiful.”

Justin Schuman, who came from Harlem to join the event, said in a voice message on Sunday that he expected to be uncomfortable at the site but that this deluge really “throws you through a loop.” He described the site on Saturday morning as “horrifically muddy.”

Mr. Schuman is staying in a structure made of insulation foam and filament tape that he built with his friends. It has withstood the rain, he said. But some other shelters around him had flooded.

People in his camp met to discuss safety and ensure that everyone had access to help if they needed it, he said.

“People are really, really, really resilient here,” he said. “If there’s one thing Burning Man people are still going to do, it’s going to be find a way to party, find a way to commune, find a way to dress up and enjoy themselves.”

Orlando Mayorquin and Eduardo Medina contributed reporting.