Texas Governor Greg Abbott has declared a state of emergency in Houston after record rainfall claimed five lives.
Meteorologists said some 17.6in (44.7cm) of rain fell on Houston on Monday alone, levels national officials said were "historic".
Rivers burst their banks in downtown Houston and 1,200 people were rescued from rising floodwaters.
Close to 70,000 people were left without power in the city, the fourth-largest in the United States.
At least 1,000 homes have flooded, with the number likely to rise. City officials have turned a large shopping centre into an evacuation centre.
As well as telling people not to drive in the fast-flowing waters, city officials warned against allowing children to play in waters that are likely to contain snakes and ants.
Among the worst-hit areas is Greenspoint, a poor, mainly Hispanic district of more than 112,000 people to the north of the city centre.
Footage broadcast in Texas showed Greenspoint families moving belongings and children through floodwaters on air beds and inside a refrigerator.
"Do not think the city is not seeing you," Mayor Sylvester Turner told Greenspoint residents in a press conference.
"It's a situation where all throughout the city, and quite frankly all throughout our region, we're dealing with high water."
At least one of those who died was found in a submerged car, local media reported.
One Houston flood official said waters recorded in one area were 40ft (12 metres) higher than the previous record.
The city, on the Gulf of Mexico, is prone to heavy rains, and has seen a number of major flooding events in the last year alone. However, this flood is the largest to strike the city since Tropical Storm Allison in 2001, which led to 23 deaths across the state, the City of Houston Twitter account said.
Mayor Turner said rains were expected to ease on Tuesday.