After the loss of her family home, Belle Reve, to creditors, Blanche DuBois travels from the small town of Laurel, Mississippi, to the New Orleans French Quarter to live with her younger, married sister, Stella, and brother-in-law, Stanley Kowalski. Blanche is in her thirties and, with no money, has nowhere else to go.
Blanche tells Stella that she has taken a leave of absence from her English-teaching position because of her nerves (which is later revealed to be a lie). Blanche laments the shabbiness of her sister's two-room flat. She finds Stanley loud and rough, eventually referring to him as "common". Stanley, in return, does not care for Blanche's manners and dislikes her presence.
Stanley later questions Blanche about her earlier marriage. Blanche had married when she was very young, but her husband died, leaving her widowed and alone. The memory of her dead husband causes Blanche some obvious distress. Stanley, worried that he has been cheated out of an inheritance, demands to know what happened to Belle Reve, once a large plantation and the DuBois family home. Blanche hands over all the documents pertaining to Belle Reve. While looking at the papers, Stanley notices a bundle of letters that Blanche emotionally proclaims are personal love letters from her dead husband. For a moment, Stanley seems caught off guard over her proclaimed feelings. Afterwards, he informs Blanche that Stella is going to have a baby. This can be seen as the start of Blanche's mental upheaval.
The night after Blanche's arrival, during one of Stanley's poker parties, Blanche meets Mitch, one of Stanley's poker player buddies. His courteous manner sets him apart from the other men. Their chat becomes flirtatious and friendly, and Blanche easily charms him; they like each other. Suddenly becoming upset over multiple interruptions, Stanley explodes in a drunken rage and strikes Stella. Blanche and Stella take refuge with the upstairs neighbor, Eunice. When Stanley recovers, he cries out from the courtyard below for Stella to come back by repeatedly calling her name until she comes down and allows herself to be carried off to bed. After Stella returns to Stanley, Blanche and Mitch sit at the bottom of the steps in the courtyard, where Mitch apologizes for Stanley's coarse behavior.
Blanche is bewildered that Stella would go back to her abusive husband after such violence. The next morning, Blanche rushes to Stella and describes Stanley as a subhuman animal, though Stella assures Blanche that she and Stanley are fine. Stanley overhears the conversation but keeps silent. When Stanley comes in, Stella hugs and kisses him, letting Blanche know that her low opinion of Stanley does not matter.
As the weeks pass, the friction between Blanche and Stanley continues to grow. Blanche has hope in Mitch, and tells Stella that she wants to go away with him and not be anyone's problem. During a meeting between the two, Blanche confesses to Mitch that once she was married to a young man, Allan Grey, whom she later discovered in a sexual encounter with an older man. Grey later committed suicide when Blanche told him she was disgusted with him. The story touches Mitch, who tells Blanche that they need each other. It seems certain that they will get married.
Later on, Stanley repeats gossip to Stella that he has gathered on Blanche, telling her that Blanche was fired from her teaching job for involvement with an under-aged student and that she lived at a hotel known for prostitution (the Flamingo). Stella erupts in anger over Stanley's cruelty after he states that he has also told Mitch about the rumors, but the fight is cut short as she goes into labor and is sent to the hospital.
As Blanche waits at home alone, Mitch arrives and confronts Blanche with the stories that Stanley has told him. At first she denies everything, but eventually confesses that the stories are true. She pleads for forgiveness, but an angry and humiliated Mitch refuses her the chance at an honorable relationship and attempts to sexually assault her instead. In response, Blanche screams "fire", and he runs away in fright.
Hours before Stella has the baby, Stanley and Blanche are left alone in the apartment. Blanche has descended into a fantasy that an old suitor of hers is coming to provide financial support and take her away from New Orleans. Stanley goes along with the act before angrily scorning Blanche's lies and behavior, and advances toward her; in response, she threatens to glass him, but is overpowered. Stanley rapes Blanche, imminently resulting in her psychotic crisis.
Weeks later, at another poker game at the Kowalski apartment, Stella and her neighbor, Eunice, are packing Blanche's belongings. Blanche has suffered a complete mental breakdown and is to be committed to a mental hospital. Although Blanche has told Stella about Stanley's assault, Stella cannot bring herself to believe her sister's story. When a doctor and a matron arrive to take Blanche to the hospital, she initially resists them and collapses on the floor in confusion. Mitch, present at the poker game, breaks down in tears. When the doctor helps Blanche up, she goes willingly with him, saying: "Whoever you are, I have always depended on the kindness of strangers." The play ends with Stanley continuing to comfort Stella, but also fondling her blouse while the poker game continues uninterrupted, as Steve says: "This game is seven-card stud."