Between American II: Unchained and American III: Solitary Man, Cash's health declined due to various ailments, and he was even hospitalized for pneumonia, and the illness forced him to curtail his touring. This album contained Cash's response to his illness, typified by a version of Tom Petty's "I Won't Back Down", as well as a version of U2's "One". Changes to Cash's voice due to his health problems are noticeable on most tracks when compared to his most recent preceding albums. Graeme Thomson has characterized "Solitary Man" as an act of emotional preservation.
American III: Solitary Man received mostly positive reviews from critics. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, the album received an average score of 80, which indicates "generally favorable reviews", based on 15 reviews. In a positive review for Entertainment Weekly, David Browne gave the album a Grade A rating, saying, "Though the Man in Black has rarely sounded blacker, producer Rick Rubin frames that deep sea voice with harmonies and churchly organs, making for a dark angel beauty of an album that's austere but welcoming." A review from Sonicnet praised Cash's ability to interpret songs and make them his own, saying, "When a tune falls into the jurisdiction of the venerable country-folk troubadour, the accumulated details of any previous readings or associations are stripped away, and its core brilliantly revealed." A review published by Billboard said the album "may lack the immediate impact of its predecessors but is no less a masterpiece." Splendid said that "the covers on American III will attract the majority of listener attention; Cash's own material steals the show."
Rolling Stone gave a mixed review, saying that "the onus here lies on the production...Rick Rubin's work is too timid; mostly, the shy combos of guitar, fiddle and accordion, or Benmont Tench's subliminal contributions on keyboards, make up the kind of severe meal that one is forced to think of as tasteful." In a mixed review, the A.V. Club said, "Like Neil Young's Silver And Gold, it feels like a thematically empty, knockabout place-holder. American Recordings, one of Cash's towering classics, was all devotion and doubt, a brilliant, raw-boned meditation on redemption and death. A loose, flat set of odds and ends, Solitary Man is merely a minor but endearing record from a man who seems to know he's given more than enough." The Spin Cycle called the album "mixed, leaning at times to inadvertent novelty."