R. A. Simpson received his education at the Christian Brothers, Melbourne Teachers' College and the Royal Melbourne Institute of Technology. He taught in secondary schools in England and Australia before his appointment in 1968 to Melbourne's Chisholm Institute of Technology where he taught Art and Literature until his retirement in 1987.
Simpson was a prominent figure in Melbourne's poetry scene and is often associated with other Melbourne poets like Chris Wallace-Crabbe and Noel Macainsh. He was poetry editor of the Bulletin (1963-65) and the Age (1969-97). His poetry has appeared in many anthologies and, beginning with Walk along the Beach (1960), he has published almost a dozen collections. A number of his later volumes also contain selections of his cubist line drawings. During the 1990s he and his work received a number of awards, including the Christopher Brennan Award (1992) and the Age Book of the Year for The Impossible and Other Poems (1998). His last book of poems, The Sky's Beach, appeared posthumously.