The younger brother of Jones Quain, Richard Quain apprenticed to a surgeon in Cork, finishing his training in London at a private medical school, and in Paris under the private lecturer Richard Bennett, to whom he became assistant. When Bennett moved to London to a post at University College, Quain came with him, eventually succeeding him in 1832 as Professor of Descriptive Anatomy. In 1848 he advanced to Professor of Clinical Surgery. In 1859 he married Ellen, Viscountess Midleton, and became surgeon extraordinary to Queen Victoria. He was also physician to many famous people, including Thomas Carlyle, Benjamin Disraeli, Edwin Landseer, and Daniel Maclise. Quain was knighted in 1891. In 1848 Quain edited, with William Sharpey, the fifth edition of his brother's Elements of anatomy. His major contribution to anatomy, however, was The anatomy of the arteries of the human body, based on 1040 post-mortem dissections. The eighty-seven life-size double chromolithographs were drawn by Quain's friend and former pupil, Joseph Maclise, and printed by Charles Graf.