Like many poets, the late Shel Silverstein used alliteration, assonance, and rhyme scheme to create rhythm and continuity in his poetry.  In "Where the Sidewalk Ends", alliteration, the repetition of consonant sounds, is scattered throughout the first stanza in the form of the "s" sound that is found in use of both the letter "s" and the letter "c".

There is a place where the sidewalk ends
And before the street begins,
And there the grass grows soft and white,
And there the sun burns crimson bright,
And there the moon-bird rests from his flight
To cool in the peppermint wind.

When spoken aloud as poems are intended to be, the listener of this poem can hear the alliteration in the words place, sidewalk, ends, street, begins, grass, soft, sun, burns, crimson, and rests. 

Assonance is the repetition of vowel sounds for the same purpose, creating rhythm, continuity, a flow of sorts in the language.  In the second stanza of this poem, assonance is found through the short "a" sound:

Let us leave this place where the smoke blows black
And the dark street winds and bends.
Past the pits where the asphalt flowers grow
We shall walk with a walk that is measured and slow,
And watch where the chalk-white arrows go
To the place where the sidewalk ends.

The assonance is found in the words black, and, past, asphalt, and shall.