Glenn Taylor is charged with criminal mischief and David Hall with aiding criminal mischief, another felony, Utah State Parks and Recreation said.
Emery County Attorney David Blackwell said he filed the charges Friday but is trying to negotiate a plea deal.
Both men, of Highland, Utah, about 30 miles south of Salt Lake City, were ordered to appear in state court March 18.
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A video shot by Hall in October and posted on YouTube shows Taylor dislodging a mushroom-shaped sandstone pillar. Taylor, Hall and another companion are then seen cheering and high-fiving.
They claimed the rock formation might have been ready to fall and kill a visitor. Taylor and Hall were later stripped of their Boy Scout positions.
Park officials have said the rock formation had been standing for much of human history, if not longer. The central Utah park is dotted with thousands of the eerie, mushroom-shaped formations.
"We are taking it seriously," Blackwell said. "It's been an interesting case, mostly because of the attention it's garnered."
Blackwell said any defense asserting the goblin-shaped rock was ready to tip over "would need to have a lot of expert testimony, and it would probably go both ways."
The round-shaped rock, which was pushed off a natural pedestal, weighed thousands of pounds, he said.
"I understand why the state brought felony charges - it's a definite deterrent effect," said Taylor's lawyer, Scott Card. "but I believe it's an overcharge. We will be defending Mr. Taylor in court."
Blackwell said Hall doesn't have a lawyer, and Hall told The Associated Press by email he had no comment at this time.
If convicted, the men could face up to five years in prison and a fine of up to $5,000.