US disaster agency says 50 counties in Texas are affected by the flooding, as weather forecasters predict more rain.
Floodwaters in parts of central Texas prompted evacuations as some areas were hit by more than 300mm on Tuesday. A state of emergency has been declared across 18 counties.
Witness videos obtained by Reuters showed heavy rain swelling the San Gabriel River in nearby Georgetown and overflowing into a park. Flooding was also seen upstream in Kingsland, Texas, where a bridge collapsed.
At least one person has died from the flooding. Local authorities warned residents to evacuate promptly on Tuesday due to strong currents threatening homes and businesses in the area.
Meanwhile, forecasters told residents along the Llano River in central Texas to seek higher ground after more than 250mm of rain fell in only 36 hours.
The National Weather Service warned that the river at Llano, about 105km northwest of Austin, rose to near-record levels on Tuesday morning.
In 24 hours, the river rose to 12 metres, some 10m higher than the day before, and around 5.5 metres above major flood stage. The record crest level is 12.6 metres set in June 1935.
A flash flood warning was put into effect, and forecasters described it as a “very dangerous situation”. It is not expected to drop below major flood stage until later on Wednesday.
Last week, four people were swept away in floodwaters along the South Llano River in Junction. The bodies of three were recovered and one person remains missing.