Pictures taken by journalist Tim Culpan on location show most of the plane submerged in water, with rescue workers using inflatable boats to reach the fuselage.
"At the moment, we think a lot of the trapped people are in the head of the plane." Unverified footage of the plane, in which its wing appears to strike a car traveling along the raised expressway, was tweeted by Twitter user Missxoxo168.
Pictures attributed to Taiwan's TVBS appear to show a taxi cab on the same stretch of road with extensive damage that could have been caused by collision with the plane's wing.
This is the second Trans Asia ATR-72 turboprop plane to crash in Taiwan in six months.
Last July, 48 people were killed when Trans Asia flight 222 crashed in Penghu, off the coast of Taiwan, after it failed to make a second landing during typhoon conditions.
Taiwanese drivers have captured the moment Trans Asia flight GE235 crashed into a river near the country's capital city of Taipei today.
The footage shows the plane, a turboprop ATR-72, rolling sharply to the left as it descends over a road.
Trans Asia Airways has confirmed that the plane carried 58 people — five crew and 53 passengers — and that at least 13 people died in the crash.
Live footage from the scene of the crash shows a number of rescue workers making efforts to extract passengers from the stricken plane, some three hours after the country's aviation authority said the crash took place.
The two fatal crashes are a blow to the Taiwanese aviation industry, which worked to make changes to its safety record after a series of high-profile crashes in the 1990s and 2000s.