Torrential rain pounding South Korea on Wednesday triggered landslides which killed 28 people and inundated hundreds of homes in the country's worst flood damage in decades.

Main roads turned to rivers of churning, muddy water, while the National Emergency Management Agency (NEMA) said that swollen streams and rivers killed an additional three people and left 10 others missing across the country.

Thirteen people died when a mudslide hit an inn and three homes in the mountainous Chuncheon area 100 kilometres (60 miles) east of Seoul early Wednesday, it said.

Fifteen people were killed the same day in southern Seoul by landslides from Umyeon mountain in the city, which was hit by 433.5 millimetres (17.34 inches) of rain in 40 hours between Tuesday and Wednesday.

Hundreds of people were forced to evacuate their homes.

A river in Gonjiam, about 30 kilometres (18 miles) southeast of Seoul, overflowed, killing three residents, the agency said.

Search and rescue efforts by more than 500 firefighters and police were still underway at Chuncheon, where ten of the victims were students from Inha University in the western city of Incheon, who were in the area for volunteer work.

"I was sleeping on the second floor of the pension (inn) when I heard the thunderous sound of a landslide. The stairs collapsed and I was buried under mud," one student rescued by firefighters told Yonhap news agency.

NEMA said 20 others were injured, four of them seriously.

In Seoul, police declared an emergency, and more than 4,000 officers were mobilised to help ease traffic gridlock, block roads deemed too dangerous to use, and aid rescue efforts.

Streets, subway stations, underpasses and residential districts were flooded throughout the capital.

"We are overwhelmed by so many rescue requests and it's not easy to keep track (of the damage)," a NEMA official told AFP.

The agency said floods or mudslides shut 37 major roads nationwide, including 23 in Seoul, and more than 700 homes were flooded in the capital. Others in the city were meanwhile prevented from leaving home by landslides or flooding.

News reports said more than 150 traffic lights were malfunctioning in Seoul, worsening the jams, while mobile phone networks were cut off in some areas.

TV images showed main streets turned into a sea of muddy water dotted with the roofs of submerged cars, with some drivers abandoning vehicles to run to safety.

Apartments and houses struck by landslides were destroyed or buried under a mass of mud, with scores of destroyed cars tossed on top of each other and tangled with uprooted trees.

Photos posted on social networking sites showed scores of cars stranded on motorways, with rising water forcing some drivers to climb onto the top of vehicles.

A video posted on YouTube showed a torrent of brown water engulfing houses and everything else on its way, with the person behind the camera yelling, "My house is almost gone!"

The Korea Meteorological Administration (KMA) forecast more downpours until Friday, with expected rainfall of up to 250 millimetres until Thursday in some areas in Seoul and nearby regions.

Rare downpours tallying more than 110 millimetres of rain per hour were recorded in southern Seoul, a KMA spokesman told AFP.