Medicine Bow is a town in Carbon County, Wyoming, United States. The population was 304 at the 2010 census. According to the United States Census Bureau, the town has a total area of 3.5square miles (9.0Square kilometers), all of it land. Medicine Bow, like many other towns across southern Wyoming, was established as a result of the construction of the transcontinental railroad in 1868. The railroad located a tie boom on the nearby Medicine Bow River and built a depot, water stop, and coal-loading facility.