The journey Blanche takes to get to Stanley and Stella's apartment when she first arrives in New Orleans is full of allusions to Greek mythology. These allusions create situational irony for the audience, as they imply Blanche is headed for heaven when she certainly isn't. She tells Eunice and the woman sitting outside the Elysian Fields house that:
BLANCHE: They told me to take a street-car named Desire, and then transfer to one called Cemeteries and ride six blocks and get off at—Elysian Fields!
Tennessee Williams named these streetcars after real conveyances in New Orleans—the streetcar which ran through New Orleans’s French Quarter really was named “Desire." Streetcars were a very popular means of getting around in the mid-20th century, meaning that "Desire" would have been a well-known cultural touchstone for New Orleans locals at this time. “Desire” would also have been deeply associated with the lifestyle and the community of the French Quarter, one of the city’s most notorious and historic neighborhoods. In order to get to the Kowalskis’s place, Blanche recounts that she had to take “Desire” from “Cemeteries” to “Elysian Fields.” In addition to referring to real things in New Orleans, these names all refer to the afterlife in Greek mythology.
In Greek legend, the Elysian Fields are the final resting place of the heroic and virtuous. They are a place of eternal reward and happiness that people favored by the gods can reach after they die. Blanche has taken a symbolic journey through death in this scene. After her life at Belle Reve and in Laurel ends, she starts her journey to the Kowalskis with “Desire.” "Desire" is both the streetcar which takes her to Stella’s apartment, and the driving force behind all of her real-life issues. She passes through “Cemeteries” to reach “Elysian Fields," which optimistically implies that Blanche has entered a sort of heaven that will end her suffering.
All of these references, though, are full of situational irony. The “Desire” which drives the actions of all the characters in this play, certainly hasn’t conveyed Blanche to heaven. Blanche's arrival at Elysian Fields, which to the ancient Greeks would represent a heavenly reward, is far from a paradise. Instead, she finds herself in a neighborhood that she finds to be dirty and frightening, and her sister is living in a way Blanche thinks is unbearable. Rather than being a safe place for her to land after she loses everything, coming to “Elysian Fields” in New Orleans only makes Blanche miserable.