South Carolina's governor says rainfalls in parts of the state have been higher than at any time in 1000 years, with at least six reported deaths as a result of the floods.
More than 35cm has fallen in three days in the historic city of Charleston.
Schools will shut on Monday and several inter-state highways have been closed.
The torrential rain has worsened by a weather system connected to Hurricane Joaquin in the Caribbean.
The storm is not expected to hit the eastern US, but the moisture associated with it is contributing to heavy rainfall.
"We haven't seen this level of rain in the low country in 1000 years. That's how big this is," South Carolina Governor Nikki Haley said on Sunday.
Ms Haley urged residents to stay indoors.
"The water is not safe and a lot of areas across the state where you see this deep water, it's got bacteria in it. So, stay inside and don't get in there," she said.
President Barack Obama has declared a state of emergency in South Carolina. The move means state and local authorities can receive federal help to deal with the flooding.
"We have every ambulance in the county out responding to calls. People are being moved from their homes in boats," Georgetown County spokeswoman Jackie Broach told Reuters.
About 100 people were rescued from their cars on flooded roads on Saturday night.
Many streets in Charleston's city centre have been closed and sandbags have been piled up to keep floodwaters out.
Violent storms and flooding have also hit south-eastern France this week, with at least 16 dead.