May Swenson's first collection of poems, Another Animal, was published by Scribner in 1954.  Her other poetry collections include A Cage of Spines (1958), To Mix With Time: New and Selected Poems (1963), Half Sun Half Sleep (1967), Iconographs (1970), New & Selected Things Taking Place (1978), and In Other Words (1987). Posthumous collections of her work include The Love Poems (1991), Nature: Poems Old and New (1994), and May Out West (1996).

Swenson’s honors include fellowships from the Guggenheim, Ford, Rockefeller, and MacArthur Foundations, as well as a National Endowment for the Arts grant. She received the Shelley Memorial Award from the Poetry Society of America, the Bollingen Prize from Yale University, and an Award in Literature from the National Institute of Arts and Letters.

In 1967, she received a Distinguished Service Gold Medal from Utah State University, and in 1987 an honorary doctor of letters. She served as a Chancellor of the Academy of American Poets from 1980 until her death. She died in Oceanview, Delaware, on December 4, 1989.