In the opening scene, Brick Pollitt (Paul Newman), a former high school football star, spends a drunken night jumping hurdles on the school athletic field in a tragic attempt to recapture his glory days. He falls and injures his right leg.
Some days later, Brick and his older brother, Gooper (Jack Carson), visit the family cotton plantation in eastern Mississippi to celebrate their father's 65th birthday on a hot and humid August day. The family rumor is that the wealthy patriarch "Big Daddy" Pollitt (Burl Ives) may have developed colon cancer and would be forced to quickly settle his will, leaving his money and land to one of his two sons before he dies.
Gooper and his shrew wife Mae (Madeleine Sherwood) have gone to great lengths to stay in Big Daddy's good favor. Gooper has lived his entire life in accordance with his father's casual instructions, and he and Mae have a "dynasty" of children to carry on the Pollitt name. Brick's wife Maggie (Elizabeth Taylor) is clever and outspoken, and holds no small amount of contempt for Gooper and Mae's entitled attitudes and five spoiled and obnoxious offspring who run around the house unsupervised. Brick, recovering from his leg injury on crutches, spends all his time in his bedroom, drinking heavily and argues with Maggie about the dismal state of their marriage. Maggie still adores Brick, though she is troubled by his self-destructive behavior, and Brick is angry and sullen towards Maggie because of a yet unspecified incident involving his recently-deceased friend Skipper. Adding to the pressure is Gooper's and Mae's constant criticism of Brick and Maggie due to Brick's alcoholism and the fact that they are childless.
Big Daddy and his wife Ida (Judith Anderson) arrive home on their private airplane from the Mayo Clinic where Big Daddy received the news that he is not dying of cancer after all. They are greeted at the airport by Gooper, Mae, and their brood of kids, but Big Daddy ignores them and is driven home by Maggie. Big Daddy is openly dismissive of Gooper's and Mae's sycophantic attitudes, knowing that they fawn over him in an attempt to secure his money and plantation for themselves. Upon arrival back at the Pollitt plantation, Brick refuses to greet his father or come down for the party, and remains in his room, drinking.
The family doctor (Larry Gates) who had previously examined Big Daddy, speaks privately with Gooper (off-camera) and Brick, confessing that he lied to the family about Big Daddy's condition to preserve their happiness for his birthday. In reality, Big Daddy really has terminal colon cancer and will be dead within a few months. The brothers initially keep the information to themselves, but Brick soon tells Maggie, who is deeply saddened.
As the evening wears on, the party wines down as it begins to rain, forcing the few guests and family inside. Big Daddy soon grows annoyed with the party and his fickle family and ventures upstairs to speak with Brick, his favorite son. He chastises him for his excessive drinking, and for his cold treatment of Maggie. Brick grows defensive and even violent when Big Daddy brings up the subject of Skipper, Brick's old football buddy who had jumped from a fifth-floor hotel window to his death a few years before. Realizing that there is more to the story, Big Daddy brings Maggie into the conversation. She explains that she hated Brick's pro-football career because he always put it before her, and that she hated Skipper for distracting Brick from his marriage. (Note: there is subtle suggestion here that Brick and Skipper had been romantically involved.) Maggie describes a drunken episode between herself and Skipper in which she considered seducing him simply to spite her husband, but reconsidered at the last minute. Brick then explains that Skipper had telephoned him, seeming to think that he and Maggie had actually made love (though he had been too drunk to remember clearly). Skipper tearfully tried to apologize to his best friend, but Brick angrily hung up on him. Skipper killed himself soon after, and Brick blamed Maggie for the tragedy. Brick angrily leaves the house as the thunderstorm rages. Big Daddy follows him out into the rain and tries to prevent his drunken son from getting into the car and driving home, but Brick angrily reveals to his father that the doctor had lied... that his illness is terminal. A shocked Big Daddy goes inside the house and down to the basement to be alone, while Brick, emotionally exhausted, is escorted back inside by Maggie.
During this time, as nearly all of the other guests have left the party, Gooper and Mae had been trying to convince Ida to settle Big Daddy's will to give them the entire estate. Ida is still unaware of her husband's condition. As Ida begins to feel stress from all the hub-bub, Mae lets slip that Big Daddy's cancer test was positive as Gooper told her minutes ago. The doctor has no choice but to admit the truth. Ida is at first overcome, but then firmly states that her husband will not be dying anytime soon, desperately trying to hold together the last traces of family unity. Maggie joins the conversation and speaks calmly to Ida to soothe her, whereas Gooper and Mae continue to hound Ida with demands. At this point, the personal rivalry between the two sisters-in-law, Mae and Maggie, becomes clear as they begin arguing with each other: Maggie reveals that she sees Mae as a dishonest, greedy, selfish, trailer-trash interloper who married Gooper solely for his parents wealth; Mae, who is pregnant with her sixth child, verbally counter-attacks with her belief that Maggie does not deserve any inheritance because she is childless and her husband drinks.
Meanwhile, Brick has put on clean dry clothes and followed his father to the cellar. Big Daddy sits in silence in his bathrobe as the apologetic doctor explains that there is no use in hiding the truth. He gives Big Daddy morphine and a syringe for the pain, and returns upstairs. Brick and Big Daddy slowly begin to rehash the past, with Brick angrily pointing out that Big Daddy's version of "family love" consists of showering his wife and sons with money and material possessions. Big Daddy admits that he indeed does not care for many of his family members, including his wife, and that he built his business to demonstrate the great things he was capable of.
After further prodding, Big Daddy recollects his own father: a boxcar tramp with no real job and no authority. Though he first speaks of his father with hostility, Big Daddy begins to smile as he remembers the fun he had as a child. He admits that he had loved his father more than anything, though he had been poor and overlooked by society. Brick becomes overwrought with emotion and trashes the basement, breaking the expensive items that his father had bought over the years to demonstrate his wealth. Once he calms down, he finally sees eye to eye with his father and the two weakened men help each other up the stairs.
Maggie, Gooper, Mae, and Ida are still in a heated conversation in the living room over Big Daddy's will, with Gooper and Mae demanding the majority of his estate when he passes on. Brick overhears his brother and sister-in-law mocking him for his drinking habit, and calmly intervenes. Big Daddy speaks to his wife with newfound respect and affection, and has adopted a positive outlook despite his condition. To halt the argument about the inheritance, Maggie tells the family that she is finally pregnant. Mae is outraged and calls her a liar, but Big Daddy and Ida are happy at the news. Brick goes upstairs and calls for Maggie. In their bedroom, Maggie thanks Brick for going along with her lie: she is not really pregnant, but wanted to give Brick's parents some hope for the future. Brick assures her that they "are through with lies and liars in this house." They lock the door and go to bed, rekindling their romance at last.