William Beare was born on 20 April 1900 in Bandon, County Cork. He is the son of William Beare and Maria Smyth. William married Sylvia Gibson on 1 August 1934 at St. Asaph, Denbighshire, Wales. Sylvia Joan Gibson was born on 9 December 1910. She is the daughter of Samuel Gibson and Rhona Hughes. They lived in Bristol, England where they were both Professors at Bristol University. William and Sylvia had three children. William died on 28 July 1963 and is buried in Bristol, England. Sylvia died on 1 June 1996 in Bristol, Gloucestershire, England.

Rhona Beare was born in 1935 in Bristol, England. She is the daughter of William Beare and Sylvia Gibson. She was educated at Clifton High School for Girls and then read Classics at Girton College, Cambridge. She then studied at Exeter University, under W F Jackson Knight, for a PhD, which she missed out on at that time. She was to get her doctorate later in 1974. She became Assistant Lecturer in Classics at Westford College, University of London and then Lecturer in Classics at Newcastle University, New South Wales, Australia. Rhona returned to Britain in 2000.

Oliver Maynard Beare was born in January 1937 in Bristol, England. He is the son of William Beare and Sylvia Gibson. He died on 9 July 1984 and is buried in Sacramento, California, United States.

Nancy Beare was born in 1939 in Bristol, England. She is the daughter of William Beare and Sylvia Gibson. She married Michael John Gregory, son of Constantinos Dmitrios Gregory and Margaret Aileen Leiper, on 8 August 1963 in Cambridge, England. They had three children. Nancy and her family live in Bristol, England.