Historically, an elegy was any poem composed of elegiac distichs (couplets) that meditated on a variety of subjects, from death to war to love. Since the sixteenth century, however, an elegy has come to mean a lament for tragedy or a mourning for the dead.

W. H. Auden's "In Memory of W.B. Yeats" uses a variety of poetic devices, some traditionally connected to the elegy and others not, to mourn Yeats's passing. While the first two sections of the poem don't use couplets, the third and final section does:

Earth, receive an honoured guest:
William Yeats is laid to rest.
Let the Irish vessel lie
Emptied of its poetry.

This, the first stanza of the third section, employs rhyming couplets with each line consisting of 7 beats. The rhyming couplets are a distinctive characteristic of the elegy.

The theme of the poem, the death of Yeats, also supports this work's categorization as an elegy. In the first section of the poem, Auden sounds as if he is addressing an audience of mourners at a funeral:

What instruments we have agree
The day of his death was a dark cold day.

The tone here is relatively subdued; Auden paints a picture of Yeats the man, describing him to those who knew him only from a distance. There's an abrupt shift in the second section of the poem, when Auden addresses Yeats directly:

You were silly like us; your gift survived it all.

There is an intimacy in this brief section, which relies heavily on figurative language and metaphor. It's as though we are being let in on an "inside joke" between the two men, like at a funeral when those close to the deceased share anecdotes to celebrate the life of the dead.

These two points—the use of the conventional elegiac meter and the subject of the poem as a meditation on death—most clearly support the reasons why we think of "In Memory of W.B. Yeats" as an elegy.