Extensive rescue efforts were under way in Seoul to get trapped residents to higher ground.
Ten of the people who were killed belonged to a college volunteer group. Officials said they were staying in a resort cabin when the mud and debris engulfed them.
Crews brought in bulldozers to help clear debris.
Witnesses said the landslide sounded like a massive explosion or a freight train. They described people screaming as buildings were carried away by rivers of mud.
About 17 inches of rain fell on Seoul and more than 13 inches on Chuncheon in the last two days, about 15 times more than the average two-day rainfall at this time of year, according to the state-run Korea Meteorological Administration.
The heavy rain also left about 620 people homeless.
The Associated Press contributed to this report.