It is clear that the tragic character in this excellent play is Blanche DuBois. From the first moment that she enters the stage, Blanche is a character who acts as a kind of catalyst to the other characters - she is met with strong reactions. Yet she is also a character who is dogged by her past which she can't ever seem to escape. We find out that she had to leave her last job in Mississippi because of an inappropriate relationship with one of her pupils and that also she used to be a Southern belle from a well-to-do family and other issues in her past that she tries to flee from.
However, as the play develops, we see that there are serious issues within the character of Blanche revealing important inconsistencies. She appears at once a kind of predatory femme fatale, flirting with Stanley and the young man at the door, but then at the same time wanting to appear fragile and wanting someone to dominate her and take care of her. In addition to this confusion, we can argue that she is obsessed with her own beauty and her past as a belle, and that being desired is incredibly important to her. She still lives in the past, thinking that she is just as beautiful now as she was then. Blanche is a paradox - the smartly dressed and cultured lady who enters the stage at the beginning is gradually shown to be a character riven by neuroses and insecurities that threaten to overwhelm her.
We cannot help but think in spite of these qualities that she is a tragic character. She seems unable to face up to the past, and all we are left with are tantalising glimpses as to what has happened. Clearly her need to constantly have baths indicates some desire to wash away the past and cleanse herself from what she has done, and yet she also finds herself unable to repeat the same mistakes. In the line that gives the play its title, she reveals indirectly her sexual indiscretion:
Haven't you ever ridden on that streetcar Desire? ... It brought me here.
We are left with a tragic character precisely because she is never able to accept herself for who she is and is split apart by her inconsistencies.