Flood water from days of intense rain flooded into the underpass so swiftly that passengers and drivers were trapped inside their vehicles, unable to flee.
In total, at least 37 people have perished as a result of flooding, landslides, and power outages across much of the country.
There are still nine persons missing.
It is unknown how many people remain trapped in the 685-metre (2,247-foot) long tunnel near the town of Osong, but 15 vehicles are believed to be buried.
Several of the remains were found inside a bus. On Saturday, nine people were recovered.
According to the family of the victims, the killings may have been avoided if the local authorities had responded effectively.
Several local media outlets stated that the river flood control office had issued a warning about the dangerously high water levels a few hours before the catastrophe, and that traffic in the tunnel area should have been redirected as a result.
The majority of the other deaths occurred in the mountainous North Gyeongsang region, where landslides swept away entire houses.
On Saturday, about 300mm (11.8in) of rain was reported to have fallen across South Korea.
According to the Korean Meteorological Association, the country receives 1,000mm (39.4in) to 1,800mm (70.9in) of rain every year, with the majority of that falling during the summer months.
Aerial photos from flood-affected areas reveal brown muck and flood levels so deep that only the tops of roofs are visible.
Evacuation orders issued by several local governments have affected thousands of people, and Prime Minister Han Duck-soo has urged the military to assist with rescue attempts.
According to the agency, some 6,400 inhabitants were evacuated early Saturday morning local time as the Goesan Dam, also in North Chungcheong, began to overflow.