Dozens of people had to be rescued from rooftops, cars and trees in the Marble Falls area 40 miles (65km) from the state capital Austin on Wednesday.
Some 18 inches (45cm) of rain fell and more downpours were predicted.
No deaths were reported in the latest in a series of storms blamed for at least 11 deaths in the past fortnight.
Mayor Raymond Whitman said there were 32 high-water rescues in the Marble Falls area on Wednesday.
He said: "If people do not pay attention and move to high ground, it is very possible that there will be fatalities."
The weather was so stormy on Wednesday that helicopter crews had to abandon four rescue attempts.
The Texas National Guard sent about 150 troops and 50 vehicles to help in central Texas.