What are some neo-classical features in Thomas Gray's "Elegy Written in a Country Churchyard"?

Neo-classicism was the dominant form in
18th-century English poetry. Such poems, often associated with the work of John Dryden and
Alexander Pope, were based on literary models provided by Greece and Rome. Since a gentleman's
education in this period emphasized learning Greek and Latin, most schoolboys would be quite
familiar with poems of antiquity written in Latin and Greek, just as we today are familiar with
movies from earlier eras, such as The Wizard of Oz (the 1930s, howeverthe
period when The Wizard of Oz was releasedare clearly
much closer to our own times than the Classical era to the 18th-century English.) The
neo-classical poems 18th-century people wrote in imitation of the Greeks and Romans  are
generally more intellectual than emotional, and characterized by measured verses in regular
rhymes.

While Gray does not address histo a single individual, which is the
standard Classical form, this poem falls into the category of "lacrinae rerum" or
"tears of (or for) things." The phrase derives from the Latin poet Virgil's
Aeneid, in which the hero looks at a mural depicting deaths in the Trojan
war, and is moved to tears. In Gray's poem, the poet feels sad as he looks at a country
graveyard, where obscure people are buried. 

In the neo-classical mode, the
tone and the rhyme scheme of a poem are measured and even, and the stance is intellectual rather
than given to emotional outburst or breaks in the cadence. The Gray poem waxes
philosophical:

Full many a gem of purest ray
serene, 

         The dark unfathom'd caves of ocean bear: 

Full many a flow'r is born to blush unseen, 

         And
waste its sweetness on the desert air.

The poem
communicates sadness, but the poet is distant from his subjects: it is sad that people die
unmourned, but that's the way life is in the larger scheme of nature.

 

The best way to understand the difference in temperament
between a neo-classically influenced poem like Gray's and a full-blown Romantic poem is to read
some of Wordsworth's work in Lyrical Ballads, such as "I Wandered
Lonely as a Cloud,"  to contrast the Romantic's outbursts with Gray's calm
verses.