Elcho had two younger brothers, Francis (1723-1808) and James (1726–1786). His sister Frances (ca 1729-1789) married Sir James Steuart (1707–1780), exiled for his part in the 1745 Rising but allowed home in 1763. He was the author of "An Inquiry into the Principles of Political Economy", described as 'one of the key economic works of the 18th century'.