The response to Close Range: Wyoming Stories and especially "Brokeback Mountain" was overwhelmingly positive. Dean Bakopoulos, in The Progressive, considers Close Range a "well-crafted collection" claiming, "this is powerful fiction, and somehow Proulx manages to give each story the plot, depth of character, sense of setting, and thematic weight of an entire novel." Rita D. Jacobs in an article for World Literature Today praises the collection's "luscious prose" and "evocative descriptions" that make "a strong impression" on the reader.

A reviewer for Publishers Weekly considers the book a "breathtaking compilation of Proulx's short fiction" that contains "an amazing, exhilarating range of mood, atmosphere and theme. Every one boasts prose that is smart, lively and fused with laconic poetry" and "her dexterity with striking images creates delights on every page." The reviewer claims that her stories are "focused by an immaculate eye and ear" and "every detail rings true" and finds a "stringent authority in her meticulous descriptions." The "distinctive impact" of Proulx's stories, the reviewer claims, is created through her "empathetic observations of the harsh conditions of her characters' lives" and "her grim awareness of the deadly accidents that can strike like lightning in the midst of exhausting daily routine."

Bakopoulos finds fault, however, with the pace of some of the stories, arguing that "on occasion, she packs in too much detail" especially in her openings. He concludes that "while impressive, this background information often slows the stories down." Jacobs insists that the stories are "uneven, but when they work, they are wondrous, with characters so alive and touching that the reader feels the ache of loss as the final page is turned."

Reviewers' highest praise is reserved for "Brokeback Mountain," which Bakopoulos calls "a tender and heartbreaking love story." He claims that its "crushing last line … sums up all the loneliness and failed dreams that make Close Range such a moving and wise collection." The Publishers Weekly review also singles out the last line of the story, noting that in its "restrained but achingly tender narrative of forbidden love" Proulx merges "the matter-of-fact and the macabre, and her summary of life's pain in a terse closing sentence, will elicit gasps of pain and understanding." Jacobs argues that "Brokeback Mountain" is the collection's "most successful" story. She concludes, "In choosing such an unlikely setting for heartbreak and creating such strongly evocative settings and characters, Proulx proves her exquisite command of the story genre."