The inspiration for Sandy came from a neighbour, a Mr Whittle, whom Humphries knew as a boy, and was portrayed in a short story, Sandy Stone's Big Week, written by Humphries (under the pseudonym H. Grahame) in 1956 but not published until 1958 (in a Canberra student magazine Prometheus). Humphries describes Sandy, originally called Dusty, as an "elderly, childless man" living in the suburbs of Melbourne. His vocal mannerisms came from an old codger Humphries met on Bondi Beach.
One of Sandy's monologues was part of the recording A Nice Night's Entertainment, which was particularly enjoyed by Humphries' friend, Peter Cook. Humphries is still writing monologues for Sandy Stone "Australia's most boring man". He said in 2016 that "slowly the character has deepened, so I begin to understand and appreciate him, and finally feel myself turning into him". He no longer requires makeup for the part, and plays Sandy in his own dressing gown.
Sandy's monologues were sometimes inspired by stories recounted to Humphries by friends or family, like the tale of Dot Swift who was handed over to the Twilight Home  which may be the very same home, or perhaps a subsidiary of the one Dame Edna's mother resides in. Barry Humphries sometimes used the character to balance pathos with humor or satire: in one monologue having the ghost of Sandy Stone recall his four-year-old daughter who died in the 1930s and how his wife then suffered a breakdown. The Australian columnist Peter Craven commented that Humphries in his Sandy Stone persona could "reduce an audience of young unbelieving cynics to tears with material that might have been written by James Joyce - delivered with wan, uncomprehending wonderment".
The character is featured in the track Sandy Agonistes on Humphries' comedy recording Moonee Ponds Muse, Vol. 1
The complete scripts (edited by Colin O'Brien) of all the Stone soliloquies were published in The Life and Death of Sandy Stone in 1990.
The artist Sidney Nolan painted a portrait of the character.