A man, Robert Mitchum, steps into a courthouse seeking out Sam Bowden, portrayed by Gregory Peck. He observes Sam during a trial before tailing him to his car, where he reintroduces himself as Max Cady. With ominous undertones, Max makes subtle threats as Sam drives away. Following this unsettling encounter, Max continues to shadow Sam and his family, even making a pass at a waitress while they are bowling. Concerned, Sam reaches out to police chief Dutton (Martin Balsam), expressing his fears about Max's creepy behavior. Sam reveals that Max is an ex-con with possible vendettas against him, raising alarms about the potential danger to his family. However, when Dutton instructs his deputies to detain Max for vagrancy, Max's knowledge of the law leads to his swift release.
The sinister tension escalates the next day when Sam discovers their dog has been poisoned. Though he suspects Max, he lacks the evidence to confront him. This leaves his wife, Peggy (Polly Bergen), and daughter, Nancy (Lori Martin), in distress. Max responds by hiring a fiery attorney, Dave Grafton (Jack Kruschen), who claims harassment by the police. Dutton informs Sam of the limitations of the law, advising him to enlist the help of private investigator Charles Sievers. Sievers (Telly Savalas) begins watching Max but fails to apprehend him during a lewd encounter, much to the frustration of the police. The woman involved with Max (Barrie Chase) refuses to cooperate and flees in fear of Max's wrath. Sievers suggests that Sam should hire a muscleman, but Sam declines.
Things come to a head the following day when Sam catches Max eyeing his daughter, prompting an altercation where Max doesn't retaliate. The tension spikes when Nancy sees Max and runs in front of a car. Though she is unharmed, Sam's anger mounts, leading him to consider obtaining a gun. However, Peggy persuades him against pursuing Max recklessly. In a desperate move, Sam encounters Max in a bar, attempting to pay him off, but Max defiantly tells him he prefers “death by a thousand cuts,” refusing the offer.
As a last resort, Sam resorts to hiring thugs to intimidate Max, but Max manages to fend them off. Boldly, Max telephones Sam to inform him that he knows he has the legal system in his corner. In a desperate gamble, Sam and Peggy devise a plan to use Nancy as bait. Sam tells Dutton he will "hide" his family on a boat in the Cape Fear River, requesting a deputy to assist in capturing Max.
The climactic showdown unfolds as Sam and Deputy Kersek (Page Slattery) lay in wait on the boat. Max emerges, catching Kersek off guard and killing him. He sends the boat, with Peggy on board, drifting away and rushes toward Nancy, prompting a frantic chase from Sam. In a fierce confrontation, Max attacks Peggy, but when Sam arrives, he diverts his attack to Nancy. The ensuing struggle leads to a dramatic fight where Sam shoots Max. Max then pleads for Sam to finish him off, but in a moment of moral clarity, Sam refuses, stating instead that Max will "rot in jail." Ultimately, the Bowden family escapes together, having faced unimaginable terror.
