Yong Chun Kim, of Tacoma, Wash., was alert, conscious and cold but otherwise stable when the team reached him at about 1:40 p.m., park spokeswoman Lee Taylor said. Weather conditions prevented a helicopter from landing in the area, and rescuers were bringing in a Sno-Cat snow vehicle to help carry him out to a paved road, she said.
Kim, who has been snowshoeing for a decade, was well equipped for a day of snowshoeing but didn't have overnight gear.
Temperatures dropped into the teens and eight inches of new snow fell in some areas since Saturday. With winds whipping on the mountain, some areas saw as much as 30 inches of snow. More snow is expected over the next few days.
"As soon as we heard he was alive, my sister, his wife, praised God and said `Hallelujah,"' Kim's sister-in-law, Sang Soon Tomyn told The Associated Press after learning from relatives that Kim had been found. "We were so worried. We prayed every day."
She said her brother-in-law was a strong hiker, had food in his backpack and knew the area very well, so they prayed he would be all right.
"He's a very strong person," she said.
Snowshoers use specialized footgear that allows them to spread their weight over a larger area, which keeps them from sinking into deep snow and makes it possible to hike into snowy areas that would otherwise be inaccessible.
Kim was leading a group of 16 members in the Paradise area, a popular high-elevation destination on the mountain's southwest flank, about a 100-mile drive south from Seattle.
He became separated from his party after sliding down a slope. Kim radioed to the group twice to say he was OK, but he failed to meet up with them in the parking lot. A search was launched Saturday afternoon.
Teams of park rangers, search dogs and volunteers combed a snowy area of Mount Rainier on Saturday, Sunday and Monday.
Because Kim was the leader of his group, other snowshoers weren't able to accurately describe where he had slipped, Taylor said.
It wasn't until Sunday afternoon that a group member could better pinpoint where Kim had fallen. Searchers had initially believed Kim fell in a different area, based on descriptions from the group, Taylor said.
Kim's son, Malcom An, thanked authorities and the rescuers in a statement released late Monday through the park service.
"A terrible situation that could have ended in tragedy, instead turned into another beautiful example of how Americans come together to help each other," he said.