There are 4 US Post Offices in Burnet County serving a total of 35,916 residents equating to 8,979 residents per post office. It's estimated that approximately 57,326 packages are handled across the 4 county post offices annually. Burnet County (/\u02c8b\u025c\u02d0rn\u1d7bt/ BUR-nit) is a county located on the Edwards Plateau in the U.S. state of Texas. As of the 2010 census, the population was 42,750. Its county seat is Burnet. The county was founded in 1852 and later organized in 1854. It is named for David Gouverneur Burnet, the first (provisional) president of the Republic of Texas. The name of the county is pronounced with the emphasis or accent on the first syllable, just as its namesake David Burnet."