Alliteration is an important part of "Landscape with the Fall of Icarus." Overall, alliteration intensifies the poem's images, bringing them to life on the page.
The first two examples of alliteration are in the second stanza:
a farmer was ploughing
his field
the whole pageantry
The poem suggests that tragedy often goes unnoticed, because most people are busy getting on with their own lives and wrapped in their own dramas. The character of the farmer introduces this idea. The alliteration between "farmer" and "field" links the man with his labor, showing how he is too wrapped up in it to notice the "splash" caused by the fall of Icarus. The two alliterative /p/ sounds are also loud and bold, pre-empting the way that the coastal town's attention is anywhere but on Icarus. It's also worth noting that the relatively methodical placement of alliteration in this stanza mimics the deliberate pattern of the farmer's plowing.
The other examples of alliteration occur in the sixth stanza (lines 13-15):
sweating in the sun
that melted
the wings' wax
The /s/ sound plays an important role in this stanza and those nearby. Sibilance is often associated with water, giving the reader a sense of the atmosphere around the coastal town. The slippery /s/, which also occurs as consonance in nearby lines, evokes the wateriness of perspiration, which relates to both the hot hive of activity in the town and, perhaps, Icarus's nerve-wracking realization that he is going to fall to his death (which presumably occurs just before the moment in which the poem is set).
The two /w/ sounds in "wings' wax" represent the way in which Icarus's wings are held together—through wax—and how they fail him.