Sir Archibald Muir or Mure of Thornton (c.1640–1701) was a Scottish merchant who served as Lord Provost of Edinburgh from 1696 to 1698.
His distant cousins included Sir Robert Mure of Caldwell was one of the jury in 1580 at the trial of Lord Ruthven for the murder of David Rizzio.
[2] On 3rd April 1696, Muir was elected to the court of directors of the Company of Scotland trading to Africa and the Indies.
[5] His daughter Margaret Muir married John Cuninghame of Caddel.
The Cuninghames of Caddel inherited the Thornton estate through this marriage, so it is deduced Archibald Muir had no surviving sons.