Tennessee Williams places his play, "A Streetcar Named Desire," in New Orleans. More specifically, the play's setting is in Elysian Fields (a working class community). The symbolism of Elysian Fields is important given it illustrates the stark contrast between what Blanche and Stella/Stanley recognize as normal.
Blanche and Stella were raised on a plantation in the south (Belle Reve). The life of the girls was very different from the life of the typical working class. When Blanche comes to Elysian Fields she finds it very hard to understand how Stella can live there.
“Stella, what are you doing in a place like that? Never, never, never in my worst dreams could I picture-only Poe!
Outside of this, Elysian Fields represents a place where life is simply accepted as it is. Not much is done to hide the shabbiness of the flats. The people living there are fully accepting of life as it is and the different types of people who inhabit it. There seems to be no classism (outside of the classism Blanche introduces) and no worries. Elysian Fields is a melting pot of people, music, and temperaments.
In the end, Elysian Fields symbolizes the realities of life (abuse, drunkenness, desire, and love).