Duncan Falls is a census-designated place in southeastern Wayne Township, Muskingum County, Ohio, United States, located on State Route 60 south of the city of Zanesville. Although it is unincorporated, it has a post office, with the ZIP code of 43734. According to the Census Bureau the population for zip code 43734 is 1200.Duncan Falls is named for an early hunter and trapper by the name of Major Duncan, who emigrated from Virginia and settled near a falls on the Muskingum River, approximately nine miles south of present-day Zanesville, in the 1790s. He reportedly skirmished with the local Shawnee over his traps, and according to legend was killed by the Shawnee while attempting to cross the river at the falls. Thus, his name became associated with these falls. Other, more mundane explanations for the origin of the town's name also exist.The settlement of the town, initially known as Duncan's Falls, began with the establishment of a store by James Taylor in 1825.