In a 1961 review of West of Your City in the Virginia Quarterly Review, James Dickey called Stafford "a real poet, a born poet." At the same time, in the Hudson Review, Louis Simpson contended that "Stafford is one of the few poets who are able to use the landscape and to feel the mystery and imagination in American life." He cited "At the Bomb Testing Site" as an example of the strength and purpose of Stafford's voice, arguing that the poet deserved wider and more serious critical attention. Critic Peter Davison in the Atlantic Monthly compared the poem to Yeats's "The Second Coming," noting its prophetic power. Stafford's work has also been likened to that of Robert Frost and Walt Whitman.

Critics over the years have tended to disagree about Stafford's standing as a poet—some accuse his "plain-style" of being repetitive, dull, or preachy; others...