As daylight dawned, some areas were submerged by flood waters, roofs were ripped from homes, and debris and fallen trees littered the streets.
More heavy rain and strong winds are predicted throughout Saturday with the authorities warning of landslides and further flooding.
More than 8,000 people were evacuated from their homes before the typhoon hit, many from southern areas prone to landslides.
Soldiers have been deployed to high risk areas and the whole island declared an "alert zone" by the authorities.
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Three people were left seriously injured with 31 reported hurt in four cities in northeast Taiwan, most of them hit by trees or flying debris.
Soulik made landfall on the northeast coast around 03:00 am Saturday (2000 GMT Friday), packing winds of up to 190 kilometres an hour, the Central Weather Bureau said.
"We expect Soulik to continue to affect Taiwan with heavy rains and strong winds throughout Saturday across Taiwan even though it is moving away and heading towards China," a weather forecaster from the bureau told AFP.
"They had to be rescued by firefighters in rubber boats after the river broke its banks. Roads are flooded and mud has been washed into homes -- this is more serious than we predicted as there has never been any flooding in Shiangshan before.
"Also an earthquake last month probably loosened the ground and triggered the mudslides," said Wu.
TV footage showed waist-deep yellow water flowing through the streets of the town of Wufeng, also in Nantou.
Streets were submerged under 30 centimetres of seawater in the port city of Keelung, the National Fire Agency said, with flooding also reported in the coastal area of Yilan and in New Taipei City, northwest of the capital.
Low-lying houses along the Hsintien River through greater Taipei were flooded, including one village where residents had been evacuated yesterday, a local police officer said.