| Miss Susan Reynolds | Year of birth 1929 | Year of death 2021 | Year elected 1993 | Fellowship category UK Emeritus |
| Mr James Ford Rhodes FBA | Year of birth 1848 | Year of death 1927 | Year elected 1911 | Fellowship category Corresponding |
| Professor Peter Rhodes FBA | Year of birth 1940 | Year of death 2019 | Year elected 1986 | Fellowship category UK |
| Rt Hon Sir John Rhys PC, FBA | Year of birth 1840 | Year of death 1915 | Year elected 1902 | Fellowship category UK |
| His Excellancy Alexandre-Félix-Joseph Ribot FBA | Year of birth 1842 | Year of death 1923 | Year elected 1916 | Fellowship category Corresponding |
| Professor Lanfranco Ricci FBA | Year of birth 1916 | Year of death 2008 | Year elected 1997 | Fellowship category Corresponding |
| Abbe Marcel Anatole Camille Richard FBA | Year of birth 1900 | Year of death 1900 | Year elected 1969 | Fellowship category Corresponding |
| Dr Audrey Richards CBE, FBA | Year of birth 1899 | Year of death 1984 | Year elected 1967 | Fellowship category UK |
| Professor Ivor Armstong Richards CH, FBA | Year of birth 1893 | Year of death 1979 | Year elected 1959 | Fellowship category Corresponding |
| Sir Rex Richards FRS, Hon FBA | Year of birth 1922 | Year of death 2019 | Year elected 1990 | Fellowship category Honorary |
| Mr Henry Richardson FBA | Year of birth 1884 | Year of death 1974 | Year elected 1952 | Fellowship category UK |
| Dr Hugh Richardson OBE, Hon FBA | Year of birth 1905 | Year of death 2000 | Year elected 1986 | Fellowship category Honorary |
| Sir John Richardson KBE, FBA | Year of birth 1924 | Year of death 2019 | Year elected 1993 | Fellowship category Corresponding |
| Admiral Sir Herbert Richmond KCB, CB, FBA | Year of birth 1871 | Year of death 1946 | Year elected 1937 | Fellowship category UK |
| Sir Ian Richmond CBE, FBA | Year of birth 1902 | Year of death 1965 | Year elected 1947 | Fellowship category UK |
| Miss Gisela M A Richter FBA | Year of birth 1882 | Year of death 1972 | Year elected 1946 | Fellowship category Corresponding |