The National Weather Service reports radar indicates some areas received as much as 8 inches of rain on Tuesday.
A flash flood warning was extended through the afternoon. The heaviest rains have moved out, but forecasters said the flood waters would be slow to recede because of the early evening high tide.
Numerous streets flooded, including those near the popular City Market and along U.S. 17 where it crosses the Charleston peninsula.
Emergency officials reported at least 20 stranded vehicles downtown where crews had to help motorists out of cars. Some businesses and homes also reported flooding.
The weather system is not related to Hurricane Isaac in the Gulf of Mexico.