Rumford is an unincorporated community in Fall River County, South Dakota, United States. It is located on South Dakota Highway 471, 19 mi southeast of Edgemont. Rumford is not tracked by the Census Bureau and shares a ZIP code (57735) with Edgemont and other surrounding towns and rural areas. Rumford was founded in 1889 when Burlington Northern extended the railroad line and built a station at this location. The railroad company changed the name from Siding No. 5 to Rumford in 1894.