Among the missing was a group who disappeared after a vacation home was swept away and slammed into a bridge.
Houston authorities recovered three more bodies from the floodwaters, bringing to 11 the number of people killed by the holiday weekend storms in Oklahoma and Texas.
Crews also searched for victims just across the Texas-Mexico border in Ciudad Acuna, where a tornado killed at least people yesterday, including an infant who was ripped from its mother's arms.
"It's absolutely massive," Texas Gov. Greg Abbott said after touring the destruction.
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Some motorists were stuck on Interstate 45 all night, sleeping in their cars.
NBA fans at a Houston Rockets game on Monday were asked not to leave the arena because of the severe weather. About 400 people remained in their seats at 1:30 a.M., choosing to stay in the building.
Some of the worst flooding damage in Texas was in Wimberley, a popular tourist town where the vacation home was swept away. The Blanco River crested above 40 feet (12 meters), more than triple its flood stage of 13 feet. It swamped Interstate 35, and rescuers used pontoon boats and a helicopter to pull people out.
The deaths in Texas included a man whose body was pulled from the Blanco; a 14-year-old who was found with his dog in a storm drain; a student who died Saturday after her car was caught in high water; and a man whose mobile home was destroyed by a reported tornado.
The Oklahoma Department of Emergency Management reported four deaths between Saturday and Monday after severe flooding and reports of tornadoes.
In Ciudad Acuna, Mayor Evaristo Perez Rivera said 300 people were treated at local hospitals after the tornado, and up to 200 homes had been destroyed.