Assonance appears in "The Kraken" most strongly in the opening quatrain, which repeats the /ee/ sound quite prominently. This long /ee/ sound is particularly noticeable because it appears in the final word of every line in the quatrain, as well as in other words throughout the lines:
Below the thunders of the upper deep,
Far, far beneath in the abysmal sea,
His ancient, dreamless, uninvaded sleep
The Kraken sleepeth: faintest sunlights flee
The /ee/ sound threaded throughout these lines creates several internal slant rhymes, as is the case in line two with the words "beneath" and "sea." This, in turn, gives the entire opening a feeling of unification and musicality that oddly contrasts with the otherwise gloomy and ominous subject. In this regard, the poem's heightened language and euphonic sound juxtapose its dark, sinister qualities.
Indeed, it is perhaps because of these sinister qualities that the pleasing assonance found in the first quatrain completely drops off in the second quatrain, as the speaker begins to focus more intensely on the Kraken's chilling environment. Indeed, as the speaker describes the Kraken's surroundings, the overall musical quality shifts considerably, veering away from assonance (apart from that seen in a few more end rhymes) and toward consonance.
This, of course, is not to say that the speaker's use of consonance isn't also musical, but this kind of musicality is much more muscular and contoured, whereas the assonance in the beginning of the poem is more relaxed. However, assonance eventually returns in line 10, bringing back the repeated long /ee/ sound that characterizes the first four lines of the poem. In this way, the sound of the poem comes full circle, ultimately developing a consistent sound that one might argue reflects the Kraken's ancient, unchanging state of rest.