Forty-five people initially survived the crash but an infant died before reaching hospital. A flight attendent sitting in the rear escaped unharmed.
Kim Hyun Shik, 20, was trapped in the wreckage of the Asiana Airlines Boeing 737-500 but managed to climb out and ran 2km (1.2 miles) to a police station to raise the alarm.
News reports said more survivors could be trapped inside the fuselage but rescuers were hampered by darkness.
An injured survivor, Moon Hyong Kun, told reporters the plane, which took off from Seoul, earlier circled two or three times over the airport of Mokpo as it tried to land. It crashed some 50 km (30 miles) to the south, an airline spokesman said.
'I was sitting in the back row. Most of the passengers in the back row escaped alive,' Mr Moon said. 'The plane descended and then flew between two hills. I fastened my belt and there was a big bang. That's all,' he whispered. 'The plane looked like crumpled paper.'
The Korea Broadcasting System said many of the dead had been flung out of the plane. It appeared they were not wearing seatbelts. State television said the plane crashed into a cliff and broke in two.
An Asiana spokesman said the twin-engined aircraft, built in 1990 and obtained secondhand last year, crashed around 6am British time yesterday after three unsuccessful attempts to land in rain and fog at Mokpo airport, 310 km (190 miles) south-west of Seoul. The cause of the crash was not known.
The spokesman said three Japanese were among the passengers but most of the others are thought to have been South Koreans.
Villagers, police and medical workers pulled the injured and dead from the wreckage and rushed them to flatter terrain. The domestic news agency Yonhap said said at least three children were being treated in hospital, two of them in critical condition.
Investigators told Yonhap a wing apparently hit the ground first, which may have cushioned the impact to some extent. The plane did not catch fire. The pilot, Hwang In Ki, had 26 years' experience, state radio said.
Weathermen said visibility at the crash site was poor, with strong winds and rain. A typhoon is expected to pass close to the south of the Korean peninsula today.