Tom, the "The Glass Menagerie's" narrator tells the audience during the opening scene, that the play is a "memory play." So everything that happens on stage is a product of his memories. Tom, a warehouse worker, lives with his mother, Amanda, and his sister Laura in a tiny apartment in St. Louis. Laura and Tom's father left the family when they were just children.

There is a tremendous amount of tension in the play, which is obvious from the first scene. Tom's mother Amanda, a woman from a genteel Southern family, has an inflated sense of herself, and unrealistic expectations for her children. The opening scene of the play gives the audience a sense of just how controlling she is. She repeatedly urges Tom to chew his food, and when Laura gets up to help clean the kitchen she urges her to sit down so that she can keep fresh for her gentleman callers. When Laura tells her that she isn't expecting any, Amanda is scandalized and recounts how she had many when she was Laura's age.

It's clear that Amanda has good intentions towards her children, but she seems to want them to pursue her dreams for them, rather than their dreams for themselves. One day, as she is on her way to a social gather, Amanda decides to stop by the school where Laura is supposed to be taking stenography classes. The school tells her that Laura hadn't attended at all since the first few classes, during which she had been so horribly nervous that she wasn't even capable of hitting the correct keys on the typewriter. Amanda is furious about it, and confronts Laura, who explains that she has been spending time in parks in museums instead of going to class because she was scared of disappointing her mother. Laura cautions Amanda that if she isn't able to support herself, she needs to start seriously looking for a spouse, because she cannot expect her brother to take care of her for the rest of his life because he will become bitter. Amanda determines that since she tried, and failed to get her daughter started on the path to being a career woman, she would need to find Laura a husband. And to find Laura a husband, she will need to fix the apartment up so that it's suitable for visitors. For this reason, Amanda gets a job selling magazines.

The family tensions come to a head when Amanda confiscates a book from Tom, who is a grown man who single handedly supports the family. Tom attempts to flee the argument by going to the movies, which is something he does frequently. Amanda accuses him of lying constantly about going to the cinema, when he is actually getting drunk. Tom says some incredibly harsh things to his mother, and she tells him that she won't speak to him until he apologizes. Infuriated, Tom attempts to flee, but in his haste he accidently breaks a one of Laura's beloved glass animal figurines. He does finally leave, and returns early the next morning intoxicated.

Laura wakes him up only an hour after he goes back to bed, and the tension between them is still palpable. Finally, Tom breaks the silence between them at breakfast, and apologizes for the unkind things that he said. Amanda has a difficult time accepting the apology, but expresses concern about both of her children. She is especially concerned about what will become of Laura, and pressures Tom to introduce her to a potential husband. Tom decides to ask a coworker at the warehouse to dinner one evening. He does not tell the man, named Jim O'Connor, that the real reason for the invitation is to introduce him to his sister, and he does not know that Laura had a crush on Jim in high school. Amanda puts a lot of money and effort into making the dinner a success.

When Jim arrives, Amanda has to cajole Laura into answering the door, and when she does, the situation is very awkward, and seeing that it is her high school crush (who does not recognize her), she flees. Tom and Jim talk while Amanda and Laura finish preparing dinner. Tom confides to Jim that he hasn't paid the electric bill for that month because he used the money to pay his merchant sailor union dues, and that he is, unbeknownst to his mother and sister, planning on leaving St. Louis soon. Amanda, Tom, and Jim have dinner, but Laura refuses to join. In the middle of dinner, the electricity goes out, but neither Tom nor Jim tells Amanda why. When they're done eating Amanda urges Jim to spend time with Laura in the living room.

The two are awkward at first, but soon begin to enjoy each other's company. Eventually Jim asks Laura to dance, which she is hesitant to do because her leg is in a brace, but she begins to enjoy it. Unfortunately, the pair dance into a table holding Laura's glass unicorn and knock the horn off it. Laura reassures him that it's okay, and notes that the unicorn is now a "normal" horse. The two talk more, and finally Jim kisses Laura, but she can immediately tell that he regrets it. He explains that he is engaged to a girl named Betty, who he has a long distance relationship with. He apologizes because, even though he likes Laura, he is committed to Betty. Laura is crushed, and Amanda is angry with Tom because she believes that he set the situation up to humiliate his family on purpose.

As the narrator, Tom explains that not long after that dinner he left St. Louis forever, and that leaving his sister has haunted him ever since.