Derek Tyndall, 21, and Thomas Dale, 20, were believed to be at about 7,500 feet on the mountain, KING-TV in Seattle reported. The mountain, 14,411 feet high, is the tallest in Washington.
The two told rangers they spent Sunday night sheltering in a cave. They had planned only a day of snowboarding but were caught by a storm that dumped 20 inches of snow on the mountain.
They used cellphones Monday morning to call for help and also called their families.
"They'll make it. There's no doubt in my mind. They're strong," said Rod Tyndall, Derek's father. "The guys have gone longer. They had a little water and a little bit of food, is what they told rangers, and they're together. They're not separated, so I have no doubt in my mind that makes them stronger as a team to get through it."