Water is so deep in places in Houston that it almost reaches signage over roads.
Much of the city’s road system has been overwhelmed by floodwaters.
Many shelters have been set up, including at a convention centre.
Officials say 30,000 people are expected to be housed in these emergency shelters.
Scores of vehicles are submerged across the city, with some owners having to be freed by emergency workers.
The coastguard has been among the rescuers working to help stranded residents.
Helicopters had to winch people up to evacuate them to safety.
Many evacuees prioritised rescuing their pets above their belongings.
Emergency 911 operators in Houston received 56,000 calls over a 15-hour time period – seven times more than during a usual working day.
Aerial photographs from the city’s high-rises show how overwhelmed Houston’s infrastructure has become.
At a news conference, the Federal Emergency Management Agency called on ordinary citizens to “get involved” in the unprecedented rescue efforts.