Nearly 20 inches of rain have fallen since Sunday night
At least five people have been killed after torrential rain closed major interstate highways and caused flooding in several parts of Houston.
Two bodies were found in a vehicle which was spotted on traffic cameras driving around barricades as the driver attempted to navigate a flooded underpass in the city.
Another person, believed to be a contractor with the city's airport system, was found in a submerged vehicle close to the airport.
A truck driver was also found dead in the cab of his vehicle after being caught in high water on a freeway service road.
The final victim was a man who was found in a submerged vehicle in Waller County. Investigators believe the car was caught up in rushing water, according to the Houston Chronicle.
Rain gauges in Harris County, which includes most of Houston, showed nearly 20 inches of rain had fallen since Sunday night.
Sylvester Turner, the city mayor, told residents to stay at home as a "stubborn" weather system continues to bring more rain into the week.
At least 1,000 people have been taken from apartment complexes in the north of the city to a shopping mall after floodwater forced them from their homes.
Harris County Judge Ed Emmett, the county's chief administrator, said thousands of homes outside Houston were flooded. At least 450 high-water rescues have been carried out.
Deputies from Harris County Sheriff's Department rescued more than 70 horses trapped up to their necks in water when their stables were flooded.
Around one million students were given the day off, with most colleges and universities also closed because of the bad weather.
At least two interstates - the I-10 and I-45 - were under water in downtown Houston.
Fire Department spokesman Jay Evans said: "When you get off the freeways and off the main thoroughfares, you could be in water 10 to 15 feet deep. You do not want to trap yourself in these vehicles."
The storms are part of a wide weather system which have left flood warnings in place for Houston, Austin, San Antonio, Dallas and Fort Worth.
Houston, which is practically at sea level, is known for its "gumbo" soft soil and is prone to flooding. Last year, heavy rains caused severe flooding in the southwest of the city.
And in 2001, Tropical Storm Allison dumped up to 29 inches of rain on parts of the city, causing $5bn in damages.