Archibald Henry Peake was an Australian politician. He was Premier of South Australia on three occasions: from 1909 to 1910 for the Liberal and Democratic Union, and from 1912 to 1915 and 1917 to 1920 for its successor, the Liberal Union. He had also been Treasurer and Attorney-General in the Price-Peake coalition government from 1905 to 1909.

The premier of South Australia is the head of government in the state of South Australia, Australia. The Government of South Australia follows the Westminster system, with a Parliament of South Australia acting as the legislature. The premier is appointed by the governor of South Australia, and by modern convention holds office by virtue of their ability to command the support of a majority of members of the lower house of Parliament, the House of Assembly.