Cunynghame is a surname, and may refer to:
Arthur Cunynghame (1812–1884), British Army officer and memoirist Sir David Cunynghame, 1st Baronet (died 1708), Scottish landowner, lawyer and politician James Blair-Cunynghame (1913–1990), Scottish banker Sir James Cunynghame, 2nd Baronet (c.1685–1747), Scottish politician Robert James Blair Cunynghame (1841–1903), Scottish surgeon and physiologist Sir William Cunynghame, 4th Baronet (1747–1828), Scottish politician