Officials predict more than 30,000 people will need temporary shelter as a result of Harvey, which is a tropical storm as of early Monday. They also expect at least 450,000 people will file for disaster assistance.
"This is a landmark event. We have not seen an event like this. ... You could not dream this forecast up," said Federal Emergency Management Agency Administrator Brock Long.
Harvey hit southeast Texas Friday as a Category 4 hurricane with winds topping out at more than 130 mph.
As of Monday, more than 3 feet of rain fell in one area outside Houston. Meteorologists say more rain is coming and that some areas might see as much as 50 inches of water when Harvey's localized storms pass.
Officials and good Samaritans have rescued people around the clock.
The Harris County Sheriff's Office performed as many as 2,000 water rescues over the weekend.
On Monday, Texas Gov. Greg Abbott activated all 12,000 members of the state's National Guard to help.
President Donald Trump issued federal emergency declarations for Texas and its neighbor Louisiana, which is bracing for possible flooding. Trump plans to visit Texas on Tuesday.
On Monday, Harvey was moving back into the Gulf of Mexico, where it's expected to strengthen a little. The National Hurricane Center predicts Harvey will then move back over Texas, dumping more rain on the Lone Star state, Louisiana, Mississippi and Arkansas.