There are 3 US Post Offices in Upton County serving a total of 3,353 residents equating to 1,118 residents per post office. It's estimated that approximately 5,352 packages are handled across the 3 county post offices annually. Upton County is a county located on the Edwards Plateau in the U.S. state of Texas. As of the 2010 census, its population was 3,355. Its county seat is Rankin. The county was created in 1887 and later organized in 1910. It is named for two brothers: John C. and William F. Upton, both colonels in the Confederate Army."