A critical appreciation of Sylvia Plath's “Circus in Three Rings” will strive to determine the poem's purpose and then evaluate how well its form and content fulfill that purpose.
Let's begin with the poem's purpose. The poet is describing her unstable mental state, trying to understand what is going on within her mind and characterize it in a way she and others can grasp.
To do this, she uses a simple form of three stanzas of six lines each. Her rhyme scheme is interesting as each stanza follows an abaab pattern. The rhythm is quite regular as well, alternating between iambic tetrameter and iambic trimeter (lines 2 and 6 of each stanza). This order actually belies the chaos of the poem and in the poet's mind and suggests that she can create and embrace patterns.
The subject matter of the poem, however, swirls wildly between images. The circus tent, the speaker begins, is a hurricane, and indeed, the images and metaphors fly by us. We have rain and weather vanes, angels and lions, a flaming rose, magicians and demons, and even “winged rabbits.” The poem ends with smoke before the speaker's eyes. This is chaos indeed, and it is all symbolic of the chaos within the poet's own mind, and it communicates that upheaval to readers in a creative way.