Steve Malone, an agent from the Environmental Protection Agency, is sent to a military base in Alabama to test possible effects on the surrounding ecological system caused by military actions. With him is his teenage daughter from his first marriage, Marti, his second wife Carol, and Marti's half brother Andy. On their way to the base, they stop at a gas station. In the restroom, Marti is threatened by an MP member with a knife. When he notices her fear, he lets go of her, satisfied that she shows an emotional response. Before she leaves the room, he warns her, "they get you when you sleep".
Steve and his family move into their new home on the base, and Marti makes friends with the base commander's daughter Jenn. On his first day in day care, Andy runs away because he is recognized as an outsider among the other somehow conformist children. He is picked up and brought home by helicopter pilot Tim. Marti and Tim quickly feel attracted to each other. Meanwhile, while examining soil samples, Steve is approached by medical officer Major Collins, who asks him about psychological effects particularly narcophobia (the fear of sleep) and their possible relation to toxication of the environment. Steve believes that a physiological reaction would be more likely.
In the evening, Marti and Jenn go to the bar attended by the station's military personnel, where they meet not only Tim but also the MP who threatened Marti at the gas station. He denies that they ever met before. That night, a group of soldiers can be seen picking giant pods from the river running by the base. When Andy wakes up and enters his mother's room, Carol crumbles to dust, while a soulless double emerges from the closet. Nobody believes Andy's story that his real mother is dead and the person pretending to be Carol is only an impostor.
The following night, Marti and her father are nearly "taken over" too by duplicates emerging from the giant pods. Carol attempts to convince Steve that the takeover is a good thing, claiming that it ends confusion and anger. She also claims that there's no place to go, as the invasion is not an isolated incident. Steve is almost shocked and saddened into compliance, but Marti and Andy drag him out the door. Carol emits a shrill and mechanical scream that alerts other "pod people" to the presence of a human being. Now the majority in numbers, they swarm over the base chasing the remaining humans.
After hiding Marti and Andy in a warehouse, Steve enters Major Collins' office. The hysterical Major tries to call for help, but the line is blocked. While swallowing sleep-prevention pills Collins announces that it is too late to run; all they can do is fight. Their conversation is interrupted by the arrival of a group of pod people, led by base commander General Platt. While Steve hides, the pod people try to convince the Major that the individual is not important, and that only conformity can solve the world's problems. The Major shoots himself rather than live in such a world.
Steve returns to his children and tells them to follow him, claiming to have found a way out. They drive aimlessly through the military base, as loudspeakers shout out instructions for spreading the invasion by carrying out pods in trucks. Realizing that her father was replicated while he was away, Marti swerves the car to the side and tries to escape with her brother. Tim, who escaped his former comrades who tried to turn him into one of them, enters the scene. Marti takes his gun and shoots the person pretending to be her father. The father duplicate shrinks into a mass of seething, bloody goo.
Tim manages to get hold of a helicopter gunship, but Marti and Andy are taken away by the pod people. They sedate both of them and take them to the base infirmary where the remaining human beings are systematically duplicated by pods. Tim is able to rescue Marti, and although Marti's half brother and Jenn, now duplicates themselves, try to stop them, they manage to escape.
The ending of the film is an ambiguous one. Tim destroys the trucks filled with pods with the helicopter's rockets, while Marti confesses her profound hatred in a voice-over narration, thereby hinting at a loss of humanitarian quality. While they land on another base, the words of Marti's stepmother earlier in the film can be heard, suggesting that the phenomenon may have already spread beyond the army base: "Where you gonna go, where you gonna run, where you gonna hide? Nowhere... 'cause there's no one like you left.