Born in Huntsville, Texas, his father was a former Walker County sheriff, but died when Elkins was just a boy.
In 1924, Elkins ventured into the banking industry, opening the Guaranty Trust Company, with just $110,000 in capital and no deposits, at a cramped location in the Rusk Building.
Corporate clients with Vinson and Elkins included Great Southern Life Insurance, Moody-Seagraves, Pure Oil, and United Gas.
Elkins was a regular attendee of the so-called Suite 8F Group (named after the room in the Lamar Hotel where gathering were held).
This behind-the-scenes socialization amongst leading Texas politicians and businessmen included the likes of Jesse Jones, Gus Wortham, James Abercrombie, George R. Brown, Herman Brown, Lyndon Johnson, William L. Clayton, William P. Hobby, Oscar Holcombe, Hugh Roy Cullen, and John Connally.