Maynard is a town in Randolph County, Arkansas, United States. The population was 426 at the 2010 census.Maynard is home to the Maynard Pioneer Museum and Park. A jail built in 1936 has a door made of wagon wheel rims. The last time it was used was in 1988, when it temporarily housed a man charged with public intoxication. The jail is beside Maynard Community Center.