The initial critical reactions in London to Glengarry Glen Ross were overwhelmingly, but not unanimously, positive. Robert Cushman in the Observer called it "the best play in London." He was especially taken with Mamet's use of language and mentioned his "fantastic ear for emphasis and repetition and the interrupting of people who weren't saying anything anyway. Nobody alive writes better American." He went on to say, "Here at last, carving characters and conflicts out of language, is a play with real muscle: here, after all the pieces we have half-heartedly approved because they mention 'important' issues as if mentioning were the same as dealing with. Glengarry Glen Ross mentions nothing, but in its depiction of a driven, consciousless world it implies a great deal."

Michael Billington in the Guardian talked of Mamet's brilliant use of language to depict character and attitudes and praised both the play and the production. Milton Shulman in the Standard praised the play and said, "There is a glib, breathtaking momentum in the speech rhythms that Mamet has devised for this pathetic flotsam." Clive Hirschhorn in the Sunday Express was not enthusiastic about the first act, but called the second act "a dazzler." Michael Coveny in the Financial Times was enthusiastic and said, "The text bubbles like a poisoned froth." Giles Gordon in the Spectator called the play "something of a let-down," and went on to say of the production that the "actors give the performances they always give."

In New York, the plaudits were even greater. The most important critic, Frank Rich of the New York Times, gave a rave review of the play and said, "This may well be the most accomplished play its author has yet given us. As Mr. Mamet's command of dialogue has now reached its most dazzling pitch, so has his mastery of theatrical form." Howard Kissel in the influential Women's Wear Daily was very positive and mentioned that, in spite of the lack of physical movement in the first act (which he likened to "some arcane Oriental puppet theatre"), the mood was not static:"intense animation comes from Mamet's brilliant dialogue, the vulgar sounds one hears on any street corner shaped into a jarring, mesmerizing music."

The headline above Clive Barnes's New York Post review read, "Mamet's 'Glengarry:' A Play To See and Cherish." Barnes called it "Mamet's most considerable play to date." He said that Mamet's language was able to "transform the recognizable into the essential," and that "the characters and situations have never looked more special." Jack Kroll in Newsweek said,"Mamet seems to get more original as his career develops," and called him,"The Aristophanes of the inarticulate.'' He went on to say, "He is that rarity, a pure writer.'' Dennis Cunningham of WCBS said, "I could simply rave to the heavens," and called Glengarry Glen Ross a "theatrical event, altogether extraordinary, an astonishing, exhilarating experience and that rarest of Broadway achievements, a major American play by a major American playwright." Douglas Watt of the Daily News found the play dull and said, "To elevate it to the status of a bitter comment on the American dream would amount to cosmic foolishness. It is what it is, a slice of life."

Glengarry Glen Ross continues to receive serious critical attention. The first book-length study of Mamet was C. W. B. Bigsby's David Mamet, published in 1985, which studies Mamet's works from the beginning through Glengarry Glen Ross. Bigsby sees Mamet as a major writer whose concern has been with "dramatizing the inner life of the individual and of the nation." Dennis Carroll's book-length study, David Mamet