In Murder in the Cathedral Eliot does not exhibit a modernist approach in the manner of Genet, Beckett, Ionesco, and many other twentieth-century dramatists. Nor can he be said to deal with specifically contemporary issues as in the realistic American theatre of O'Neill, Miller, or Williams. His play is rather a meditation on English history and freedom which, though set in a specific time and place, seems to exist in a world of its own, much as Eliot's poems such as "The Waste Land" and "The Four Quartets" do.
This does not mean the play lacks "realism." But if you wish to find elements in it that relate somewhat to the usual definitions of modernist drama and even Theatre of the Absurd, you can look at the scene in which Becket is killed, and at the manner in which the knights try to justify the murder. Their speeches become increasingly artificial and convoluted. They repeat stock notions such as their appeals to the English sense of "fair play," and so on. The overall effect, in my view, is a satiric one, out of key with most of the play, and deliberately absurd. Like most authors, Eliot is utilizing past events in order to find modern meanings in them. Yet one only has to compare his play with the 1964 film Becket (which is a conventionally realistic portrayal of the same period) in order to see that although Eliot was not part of the modernist movement per se, his treatment of the murder of Thomas Becket is anything but conventional.