Elba is an unincorporated community in Cassia County, Idaho, United States, that is located along Idaho State Highway 77 Spur. Elba was originally called Beecherville, and under the latter name the first permanent settlement was made in 1873. A post office named Elba was established in 1883, and remained in operation until 1996. The preseā¦Elba is an unincorporated community in Cassia County, Idaho, United States, that is located along Idaho State Highway 77 Spur. Elba was originally called Beecherville, and under the latter name the first permanent settlement was made in 1873. A post office named Elba was established in 1883, and remained in operation until 1996. The present name is a transfer from the island of Elba, in Italy.