More heavy rain with potential for additional flooding was forecast.
The raging waters destroyed hundreds of homes and sent cars floating down streets, rolling and bobbing like giant toys.
In the Texas city of San Marcos, residents were ordered to evacuate their homes as flood waters rose menacingly around them, following torrential rain that turned streets into meandering rivers.
Cars and trucks were submerged and people used inflatable lounge chairs to float down the street, in surreal scenes.
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In Texas at least 12 people are reported missing, said Kharley Smith, emergency response coordinator for Hays County, which includes San Marcos.
She said people were forming their own search parties along the Blanco River, and warned them against this, saying it was dangerous.
"We have local resources, regional and state assets that are actively doing search and rescues. It's not safe for the general public to go down and do those rescue or search operations themselves," Smith told a news conference.
Fire Marshal Ken Bell told CNN that at least one person was confirmed dead and crews were searching for three missing people.
At least two people also died in Oklahoma, which is located to the north of Texas.
A firefighter in the town of Claremore died when he was swept into a storm drain while trying to help a resident in floodwaters, CNN said, and a woman in Tulsa died after her car hydroplaned.
The National Weather Service warned that strong to severe thunderstorms were expected across a large stretch of the central and southern plains toward the Mississippi River Valley.