One thing that defines a piece of literature as a classic is its influence on other writers. Paradise Lost has had that kind of lasting influence on such writers as William Blake, Mary Shelley, and C. S. Lewis. One critic has noted that
More than any other literary forebear, John Milton's Paradise Lost stands as a continuing intellectual and mythic reference point for Mary Shelley's Frankenstein. (see the Univ. of Penn. link below)
To many people during the 18th and 19th centuries, Paradise Lost was almost as important to have as the Bible. The Norton Anthology of English Literature states that "Paradise Lost was often one of the very few books found in British and American households."
See also the eNotes critical overview of the poem (linked below).
Aside from Beowulf, Paradise Lost is the first poem of epic proportions to be published in England.
It is considered a classic for several reasons, one of them being the enormity of the task in rewriting the creation story of the Bible. The language is beautiful and captivating, and he tells the story from different points of view--Adam, Eve, the Serpent, etc.
In addition, as with any "classic", Milton asks the important and difficult-to-answer questions that others may shy away from due to their controversial nature. Some of these are listed in the enotes summary, and are as follows:
If the world was created by a good, just, and loving God, why is there little evidence of goodness and justice in the world? What does it mean for humankind to be created in the image of that God, and how does humanity endure in a fallen world?
Follow the link below to read more about Paradise Lost.
There are many aspects that could be explored as to why this piece is a classic.
For starters, Paradise Lost is a classic because it is the first true English epic. Milton was successful in joining the ranks of other classic writers, such as Homer(Greek)-who wrote the Odyssey and the Iliad, Virgil(Latin)-who wrote the Aeneid, and Dante(Italian)-who wrote the Inferno.
Paradise Lost explores Adam and Eve's creation and their fall from grace. Milton was praised for his use of language and characterization.