More than a foot of rain had fallen by Monday evening in parts of Houston, submerging scores of subdivisions and several major interstate highways, forcing the closure of schools and knocking out power to thousands of residents who were urged to shelter in place.
At least five fatalities appeared to be weather related, authorities said.
Sylvester Turner, mayor of the nation's fourth-largest city, told residents to stay home to fend off a weather system he called "stubborn." More rain was projected over the next two to three days, although heavy downpours had subsided and only another half-inch was expected through Monday night, he said.
Rain gauges in parts of Harris County, which includes most of Houston, showed water levels approaching 20 inches since late Sunday night, with slightly smaller amounts elsewhere in Southeast Texas as bayous and creeks overflowed their banks.
Harris County Judge Ed Emmett, the county's chief administrator, said two bodies were found in a vehicle shown on traffic cameras driving around barricades and unsuccessfully attempting to navigate a flooded underpass.
In addition, one person, believed to be a contractor with the city's airport system, was found in a submerged vehicle not far from the airport. A second person, a truck driver, was found dead in the cab of his rig after encountering high water on a freeway service road.
In nearby Waller County, a man was found in a submerged vehicle, which investigators believed was caught in rushing water, the Houston Chronicle reported.
Several shelters were established for people forced from their homes. At least 1,000 people taken from apartment complexes in the north part of the city and moved to a shopping mall were being ferried by city buses to a shelter, the mayor said.
Emmett said thousands of homes in the county outside Houston were flooded, many for the first time. At least 450 high-water rescues were conducted, he said.
One man on the city's north side emerged from flood waters carrying an armadillo by its armoured tail to safety.
In another animal rescue, deputies from the Harris County Sheriff's Department livestock unit used boats to reach an estimated more than 70 horses trapped up their necks in water when their stables were flooded.
About one million students got the day off, including the Houston Independent School District's 215,000 students, Texas' largest public school district. Most colleges and universities also closed because of the bad weather.
Major roadways treacherous
Dozens of Houston subdivisions flooded. At least two interstates — I-10, the main east-west freeway, and I-45, the major north-south freeway — were under water near downtown.
Other major freeways, plus some feeder roads leading to the highways, were blocked by high water.
"I was trying to get to work," Marcel Gwinn said as he was stranded for more than 90 minutes on an overpass in west Houston. "It kills me because my boss just told me that work's closed for the day."
Immediately to the north of Houston in Montgomery County, more than 260 water rescues were carried out, county emergency management officials said.
"When you get off the freeways and off the main thoroughfares, you could be in water 10 to 15 feet deep," Fire Department spokesman Jay Evans said. "You do not want to trap yourself in these vehicles."
One TV reporter in Houston helped to rescue a man who drove his car into a flooded underpass.
In the incident captured on video Monday, KTRK reporter Steve Campion yells, "Dude, you've got to get out of the car!" The man opens the passenger door and crawls out into the water as the reporter yells: "Leave the car! Swim!"
The driver swims toward Campion, who wades out into the waist-deep water and extends his hand. As the car slowly sinks under water, the driver tells Campion that he's OK and that he didn't think the water was so deep.
The storms were part of a wide weather system that left warnings and watches through Tuesday morning for Houston, Austin, San Antonio, Dallas, Fort Worth, Tyler-Longview and as far east as Texarkana.
Houston, at near sea level and known for its "gumbo" soft soil, is no stranger to flooding from torrential rains, tropical storms and hurricanes. Last Memorial Day, heavy rains caused severe flooding in the southwest parts of the city. Bayous that last year overflowed after 25 centimetres of rain quickly rose again, putting water in at least 200 homes, the mayor said. They appeared to be receding slightly by Monday evening.
In 2001, Tropical Storm Allison inundated parts of the city by dumping over 70 centimetres of rain, causing $5 billion US in damages.
"A lot of rain coming in a very short period of time, there's nothing you can do," Turner said. "I regret anyone whose home is flooded again. There's nothing I can say that's going to ease your frustration. We certainly can't control the weather."