The National Weather Service said the area could get an additional 2 to 4 inches of rain this afternoon and a flash flood warning remained in effect.
Police say numerous streets have been flooded, including those near the popular City Market and along U.S. Highway 17 where it crosses the Charleston peninsula.
Emergency officials reported at least 20 stranded vehicles in the downtown area, where crews had to help motorists out of their cars. The Citadel canceled evening classes because of concern the flooding would be aggravated by the early evening high tide.
The weather system is not related to Hurricane Isaac, which is moving toward landfall in Louisiana.