In the Victorian period, two young cousins, Richard and Emmeline Lestrange, and a galley cook, Paddy Button (Leo McKern), survive a shipwreck in the South Pacific and reach a lush tropical island. Paddy cares for the small children and forbids them by "law" from going to the other side of the island, as he found evidence of remains of bloody human sacrifices. He tells them the bogeyman lives there as a way to make sure they do not go there. He also warns them against eating a certain scarlet berry Emmeline has found which is apparently deadly.

Paddy soon dies after a drunken binge and his body is discovered by Richard and Emmeline. Now alone, the children go to another part of the island and rebuild their home. They survive solely on their resourcefulness, skills that Paddy had taught them and the bounty of their remote paradise.

Years pass and they both grow into tall, strong and beautiful teenagers. They live in their hut, spending their days together fishing, swimming and diving for pearls. Richard and Emmeline (now portrayed by Christopher Atkins and Brooke Shields) begin to fall in love, although this is emotionally stressful for them because of their lack of education on human sexuality, and are unable to express their physical attraction for one another. Emmeline is frightened after she begins her first menstrual period, and is nervous when Richard wants to inspect her for a cut. Richard himself has many questions about what is happening to them as they begin to grow and develop, but has no means of getting answers. He wishes to hold and kiss her, but when she rejects him he goes off and masturbates.

Emmeline, ever curious, goes to the other side of the island and discovers an impressive, Moai-like idol there. Instinctively recognizing that this is a holy place, she prays. Later she tells Richard that she thinks Paddy was wrong and the "bogeyman", who bleeds like Jesus, is actually God. However, Richard berates her for disobeying the "law".

Sometime later, their relationship suffers a major blow when a ship appears for the first time in years. Richard's desire to leave comes into conflict with Emmeline's desire to stay, and she does not light the signal fire. As a result, the ship passes by without noticing them. Richard's fury leads him to kick her out of their hut. They make up for this fight after Emmeline is nearly killed upon stepping on a stonefish and Richard admits to his fear of losing her. Emmeline eventually recovers and after she regains her ability to walk, they goskinny dipping in the lagoon and then swim to shore. Still naked, Richard and Emmeline share some fruit in the vegetation overlooking the idol, and discover sexual intercourse, and thenpassionate love. Casting all their unease aside, they regularly make love from then on while occasionally spending their time together in the nude. Due to their regular sexual encounters though, Emmeline soon becomes pregnant. Although this is clear to the viewer, Richard and Emmeline themselves do not know about the truth of childbirth and human reproduction and simply assume that the physical changes in Emmeline's body is her getting fat. They are also stunned when they begin to feel the baby move inside Emmeline and simply assume it's her stomach causing the movements.

One night Emmeline goes missing. While Richard looks for her in the forest, he witnesses a human sacrifice committed by the natives of another island at the idol shrine where they sacrifice some enemy natives. As he flees, Richard hears Emmeline cry out and follows the sound just in time to help her give birth to a baby boy, whom they name Paddy, in remembrance of Paddy Button. Later on, frustrated at not knowing how to feed the baby, Emmeline holds him in her arms to appease his crying, and learns how to feed him as the baby instinctively starts sucking on her breast. The young parents spend their time playing with Paddy as he grows, teaching him how to swim, fish and build things and happily raising him.

As the family plays, a ship led by Richard's father Arthur (William Daniels), approaches the island, and sees the family playing on the shore. As they are completely covered in mud, Arthur assumes these are natives, not the young couple they have been searching for all these years. Richard, having lost all of his desire to leave the island, agrees with Emmeline with an exchange of glances, and they let the ship pass (not realizing that Arthur is on the ship).

One day, the young family takes the lifeboat to visit their original homesite. While waiting for Richard, Emmeline and Paddy remain in the boat. Emmeline falls asleep and does not notice when Paddy brings a branch of the scarlet berries into the boat. She awakes as Paddy tosses one of the oars out. The tide was sweeping the boat out into the lagoon and Richard, hearing her calling, swims to her, followed closely by a shark. Emmeline throws the other oar at the shark, striking it and giving Richard just enough time to get into the boat. Though close to shore, they are unable to return or retrieve the oars without risking a shark attack. They paddle with their hands, but to no avail; the boat is caught in the current and drifts out to sea.

After drifting for days in the boat, Richard and Emmeline awake to find Paddy eating the berries he picked. Realizing that these are the poisonous berries Paddy warned them about, they try to stop him, but he had already swallowed a few. Hopeless, Richard and Emmeline eat the berries as well, lying down to await death. A few hours later, Arthur's ship finds them floating in the boat. Arthur asks, "Are they dead"? and the ship's captain (Alan Hopgood) answers, "No, sir. They're asleep". And Arthur is relieved.