Alliteration is used frequently in "Beach Burial." For instance, it's prominent in lines 2 and 3:
The convoys of dead sailors come;
At night they sway and wander in the waters far under,
The alliteration here, coupled with consonance, gives lines a sense of ebb and flow that conveys the way that the dead men's bodies drift helplessly on the tides.
Then, in line 6, the alliteration of "Someone" and "seems" has a whispery, watery sound—like a sea breeze (other /s/ consonance in this stanza adds to the effect).
The next example is in line 7, with "bury" and "burrows." These two /b/s sound insistent, emphasizing the determination of "someone" to see that the men get some kind of makeshift burial—even if it is in shifting sands and with crosses made of driftwood.
Next up is line 11:
Written with such perplexity, with such bewildered pity,
The alliteration here draws the reader's attention to the material construction of the line, the fact that is something written. This in turn supports the starkness of the image of the makeshift crosses and the writing upon them. The repeating sounds also give the line a dense feeling, reinforcing the idea that whoever wrote the words had to push through confusion and pain in order to do so.
In line 17, three /s/ words alliterate ("seaman," "search, and "same"). This sibilant sound is associated with the sea, and so its repeated use evokes the endless—eternal—search of the men for the peace of the afterlife.