To write a critical analysis of a poem, we first want to make a decision on the overall theme of the poem. We then want to literally criticize the poem, meaning "judge [its] merits and and faults" (Mississippi Gulf Coast Community College, "Learning Lab Tips on Critical Analysis--Poetry"). To critique the poem, we'll be analyzing its literary devices, such as "imagery, metaphor, poetic language, rhyme scheme," etc. and deciding how effectively or ineffectively the poet used these devices to illustrate the theme ("Learning Lab Tips"). We will specifically be asking ourselves the questions, "What is the poet trying to say? How does he or she try to say it?" ("Learning Lab Tips").
T. S. Eliot's poem "Gus: The Theatre Cat" certainly offers many different ways in which we can interpret the central theme. Since the story is about an elderly cat who takes pride in telling the story of his past glorious theater days, we might conclude the poem is simply intended to instruct the reader on the acceptance of old age and the importance of living life to the fullest while young.
Or, we might question exactly why T. S. Eliot chose to characterize a cat as an actor. It is known that in England, even prior to Shakespeare's days, cats were considered good luck to theater houses. Just like sailors considered cats good luck and kept them on their ships as both rat catchers and companions, theater managers also kept cats and used them for keeping the theater rodent free. Shakespeare even makes numerous references to cats in his plays and most likely made use of quite a few cats himself. Hence, Eliot's allusion to cats in the theater isn't as fantastical as it seems at first glance, and we might even conclude that Eliot's primary theme is focused on praising theater and how it transforms lives.
Some literary devices that may help us analyze and critique the first theme can include the imagery Eliot uses to describe the cat in his old age, such as the phrases "coat's very shabby," "thin as a rake," and "palsy that makes his paw shake." It can be argued that Eliot couples imagery to describe Gus in a dilapidated state with diction to portray Gus as a star in his glory days, such as the diction in the phrase "Star of the highest degree." We could further argue in our thesis statement that the coupling of imagery and diction effectively illustrates the theme of acceptance of old age and the necessity of living life to the fullest.
If we want to argue that the theme is to praise theater as influencing lives, we can refer to all of the many theater-based allusions found in the poem, such as Irving, Little Nell, and Shakespeare.