The entire play is set on a park bench in Central Park.
One Sunday afternoon, Peter, an upper-middle-class family man and publishing executive in his mid-forties, is reading a book on a bench. Jerry, a sloppily dressed transient in his late thirties, approaches and announces that he is coming from the Central Park Zoo. Despite Peter’s apparent reluctance to chat, Jerry strikes up a conversation. Jerry’s forward personality quickly begins to annoy Peter – he points out that Peter will likely get cancer from smoking, and implies that Peter is emasculated because he has cats instead of dogs.
Jerry continues to ask Peter questions about his life, his job, and his interests. When Peter finally begins to return Jerry’s questions, Jerry tells him about his miserable apartment in a flophouse on the Upper West Side. He describes his unsavory neighbors and the junk that comprises his possessions – including two empty picture frames. When Peter asks him about the picture frames, Jerry explains that he is completely alone in life. His parents died when he was young, and his only significant romantic relationship was a short liaison he had with another boy when he was a teenager.
Jerry promises to tell Peter about his trip to the zoo, but is sidetracked into telling Peter about his landlady, a drunken woman who constantly propositions him. When she got a dog, Jerry tried to befriend it, but the dog responded only by attacking him. After repeated and repudiated attempts at friendship, Jerry decided to murder the dog by feeding it a poisoned hamburger patty. Although this sickened the dog, it eventually recovered and began to simply leave him alone.
Peter finds this story extremely disturbing, and wonders why Jerry told it to him. Jerry explains that he tries to befriend animals as a gateway to befriending other people.
Peter tries to excuse himself, but Jerry tickles him to keep him from leaving. He then tries to force Peter to move from the bench, and punches him when he refuses. Although Peter initially realizes that Jerry’s behavior is absurd, he gradually becomes more possessive of the bench.
Jerry pulls a knife and insists the men fight for it. This shocks Peter, who refuses to fight. As a gesture of peace, Jerry gives the knife to Peter, who holds the knife out to protect himself. Suddenly, Jerry charges Peter and impales himself on the knife.
Although he is initially hysterical, Jerry soon calms down and accepts his death. He even thanks Peter, using his last energy to wipe Peter’s fingerprints off the knife handle so that Peter will not be accused of his murder. Peter takes his book and dashes off before passers-by notice that Jerry is dying.