The third typhoon to hit Taiwan this month has killed at least four people and injured hundreds, knocking down trees and cutting power to millions.
On Tuesday, most schools and offices were shut and the north-south bullet train suspended services as Typhoon Megi, packing winds of well over 160km/h, roared in from the Pacific.
Major cities in Taiwan announced schools and offices would be shut for a second day on Wednesday as the island's weather authorities said that due to the large diameter of the typhoon, heavy rain and strong wind would not significantly abate until Wednesday afternoon.
At least 329 people were injured and more than 14,000 evacuated, the government's Central Emergency Operation Centre said late on Tuesday.
Authorities also estimated more than three million households had lost power, while over 72,000 were without water.
Taiwan's financial markets, which were shut on Tuesday because of the storm, will also be closed on Wednesday, financial regulators said.
Hundreds of international flights were cancelled or delayed, while train services, halted were scheduled to be suspended until Wednesday afternoon.
A tour bus carrying 29 passengers from a Japanese tour group was knocked onto its side on the highway by strong gusts, injuring some of the tourists, transportation authorities said in a statement.
Local television footage showed the tourists climbing out of the bus through its windshield, while other TV footage showed trucks also knocked sideways on the highway and scaffolding ripping away from a building in central Taiwan.
The typhoon moved across Taiwan and is heading into the Taiwan Strait before it is expected to make landfall in China in its southeastern province of Fujian.
China's Ministry of Civil Affairs said it had ordered authorities across a swathe of southern and eastern China to step up disaster prevention preparations.
This month, super Typhoon Meranti killed at least 28 people in China and Taiwan and cut power to more than a million homes.