I would not argue that it would be best to classify it as a classical tragedy because of its themes and structure, but one could certainly identify many of the elements of classical tragedy in the play. For example, even though Willy Loman is not a once noble hero, he does have a tragic flaw; he does experience a tragic realization, and he certainly has a tragic downfall--all classical tragedy features.
"Death of a Salesman" by Arthur Miller sets a sad tone of failure and misfortune as Willy looses his grasp on achieving the American Dream. For a written work to be considered a classical tragedy five basic components should be present; a tragic hero, a tragic flaw or misjudgment, a belief by the hero that he can outwit fate or go against a moral law, a catastrophe or changing event, and a turn of events from fortune tragedy. In looking at these components one must determine if these are present within the play.
-Willy meets the criteria as a tragic hero. He has spent his life struggling for something good for his family. He has gone in quest of the American dream armed with his ability to sell insurance. He has stuck it out and braved the changing tides of the industry.
-Willy makes the mistake of trying to end his life in ways in which he does not succeed.
-Willy has always believed that if he worked hard enough he would earn the American dream for his wife and family and own his own home.
-Willy runs off the road and dies.
-Willy’s death has caused his family to achieve the American dream of owning a home, but Willy will never get to participate in reaching the American Dream himself because without his death, the family would not have had the house paid off by his insurance.
After looking at these factors one could state with reason that the “Death of a Salesman” meets the criteria as a classical tragedy.