Rapid Creek is a tributary of the Cheyenne River, approximately 86 mi (138 km) long, in South Dakota in the United States. The creek's name comes from the Sioux Indians of the area, for the many rapids in the stream.

The Cheyenne River, also written Chyone, referring to the Cheyenne people who once lived there, is a tributary of the Missouri River in the U.S. states of Wyoming and South Dakota. It is approximately 295 miles (475 km) long and drains an area of 24,240 square miles (62,800 km2). About 60% of the drainage basin is in South Dakota and almost all of the remainder is in Wyoming.