Capt. Henry Bayard Rich (14 June 1849 – 17 November 1884) was a British soldier, who played for the Royal Engineers in the 1872 FA Cup Final. As a soldier, he saw active service in three campaigns: the Perak Expedition of 1875–76, the Zulu War of 1879 and the Egyptian Expedition of 1882. He was killed in an accident while playing polo.
Rich was born in Berbice, British Guiana, the first child of Col. Frederick Henry Rich (1824–1904) and his wife Elizabeth née Bayard (1826–1885). His father became a Colonel in the Royal Engineers and was the Chief Inspecting Officer of the Railway Inspectorate between 1885 and 1889. His mother was the daughter of Richard Henry Bayard, US Senator and Chief Justice of Delaware.
Rich was educated at Marlborough College between April 1864 and Christmas 1866. He was then trained at the Royal Military Academy, Woolwich between 1867 and 1870.
Rich played football for Marlborough College and RMA, Woolwich before joining the Royal Engineers. He generally played as a forward and was "ranked as one of the best football players of his day" who "strove hard to pass the backs".
In November 1871, the Royal Engineers were among fifteen teams who entered the inaugural FA Cup competition; after victories over Hitchin (5–0), Hampstead Heathens (3–0) and Crystal Palace (3–0 after a replay), the Engineers met Wanderers, the top amateur club of the day, in the first FA Cup Final, played at Kennington Oval on 16 March 1872, which the Engineers lost 1–0, to a goal from Morton Betts.