What is the role of male dominance within A Streetcar Named Desire?

The role of male dominance within Williams' A Streetcar Named Desire is exemplified through the character of Stanley. Throughout the play, Stanley consistently exerts his dominance over his fellow characters through the use of extreme control. For example, when Blanche first arrives at the Kowalski's tiny home, Stanley instantly insists on investigating her background and determining her financial status. He frequently tells Stella of the "Napoleonic Code," believing that Blanche sold the family estate of Belle Reve but kept the profits for herself. In his mind, this essentially means that Blanche stole from him, not Stella, which is unacceptable. As the "man of the house," he feels that it is his responsibility and duty to right this wrong, regardless of Stella's feelings on the matter.
Stanley also exerts emotional dominance over his fellow characters by maintaining complete control over each situation that arises. For instance, when Blanche first arrives, Stanley is determined to maintain control over the relationship between Stella and her sister, frequently trying to undermine any bond that develops between the women. He rifles through Blanche's things to prove she is lying to her sister, and he questions everything Blanche says, so that it becomes impossible for Stella to fully trust her: "Sit there and stare at me, thinking I let the place go? I let the place go? Where were you! In bed with your–Polack!" (Williams, Scene 1). Stanley also proves dominance over the relationship between Blanche and his friend Mitch. When Mitch becomes attached to her, Stanley steps into assert his control over Blanche by sharing all of her rather sordid history with Mitch, making Mitch decide to leave Blanche. This effectively removes Blanche's last vestige of hope, so that she is once again firmly entrenched in Stanley's control with no escape.
In addition to emotional control, Stanley also asserts his dominance sexually. He is described as almost animalistic in his overt sexuality, which is the primary draw that pulls Stella to him in the first place: "Since earliest manhood the center of [Stanley’s] life has been pleasure with women, the giving and taking of it, not with weak indulgence, dependently, but with the power and pride of a richly feathered male bird among hens" (Williams, Scene 1). After he abuses Stella, she takes him back pretty quickly and tells Blanche the morning after that she really can't help herself, proving that the animal sexual attraction of Stanley gives him complete control over her. Stella claims, "There are things that happen between a man and a woman in the dark–that sort of make everything else seem–unimportant" (Williams, Scene 4). In contrast, Stanley asserts sexual dominance over Blanche by frequently making her sexually uncomfortable throughout the play, sometimes even threatened, culminating in their destined "date" when he rapes Blanche while Stella is in the hospital having his child.
Furthermore, Stanley asserts physical dominance over both women throughout the text, beginning in one of the very first encounters when he throws a chunk of meat at Stella for her to prepare for him. His physical dominance grows stronger as the story progresses, frequently breaking things, shouting, and booming at the people in his life. In Scene 4, Stanley's physical dominance progresses to the point of striking Stella for not turning down the radio when he ordered her to do so. It took his friends restraining him to keep him from harming her further. In this scene, Stanley's dominance over his wife becomes poignantly clear, as all it takes is a shouted apology for her to go back to him. His physical dominance climaxes at the end of the play in his treatment of Blanche, when he rapes her. His dominance over his wife is so strong that she chooses to believe him over Blanche and send Blanche to an asylum, rather than standing up to her husband.

In A Streetcar Named Desire, Stanley Kowalski is the personification of the alpha male type of masculinity. He's tough, physically imposing, and protective. He is also dominant. Indeed, his dominance over his wife, Stella, is such that she sides with him after he hits her and even after he rapes her sister, Blanche. This dominance is largely because Stella is attracted to all of Stanley's aforementioned alpha male characteristics. Stanley's role as the alpha male, and the dominance over his wife that that role entails, is demonstrated early on, when Stanley throws a piece of meat up to Stella. He is here presented as the caveman, bringing meat back from a hunt and presenting it to his woman to cook it for him.
Stella seems to adopt her submissive role in this relationship just as readily as Stanley adopts his dominant role. From a modern perspective, Stella's acceptance of submissiveness might appear strange. One might infer that these roles are simply genetically hard-wired into men and women respectively. Or one might infer that this imbalanced relationship, built upon male dominance and female subservience, had simply become hard-wired, as it were, into the genetic makeup of early twentieth-century American society.
When Stanley rapes Blanche, we are shown a literal, violent manifestation of the usually more latent aggression and violation of everyday male dominance. In this scene, which actually takes place off-stage, he violates her physically but also psychologically. In fact, the psychological violation is so severe as to send Blanche spiraling into madness. And while the rape is, of course, an extreme manifestation or consequence of male dominance, it is a manifestation nonetheless. Stanley feels that he is within his rights to rape Blanche because he takes for granted the dominant position of the male in 1940s American society.