A jaded pilot named Noah Dugan (Elliott Gould) is unemployed and owes a large amount of money due to his gambling. He goes to an old friend, Stoney (Vincent Gardenia), who owns an airfield. He is offered a job flying a cargo of animals to a remote South Pacific island aboard a B-29 bomber, a large plane well past its prime.[Note 1] Bernadette Lafleur (Geneviève Bujold) is the prim missionary who accompanies him. Bernadette has raised the animals at an orphanage and is close to two of the orphans, Bobby (Ricky Schroder) and Julie (Tammy Lauren).
As the aircraft prepares to taxi for takeoff, Bobby is concerned about Dugan’s treatment of the animals, and decides to stow away aboard the bomber so that he can make sure his special friends are properly cared for. Julie follows Bobby aboard. During the flight, the bomber goes off course, and Dugan is forced to crash-land on an uncharted island that Bobby has spotted with his keen eyesight. While on the island, the group meets two elderly Japanese holdout soldiers who have lived there alone for 35 years. Dugan treats them as enemies, as the soldiers are unaware that World War II is over, but Bernadette wins their friendship and trust. They are able to communicate because the mother of one of the soldiers had spent time in America, and she taught her son how to speak English. She even named him “Cleveland”, after her favorite place there.
The soldiers convince Dugan and Bernadette that there is no hope of rescue should they stay on the island, as the two had been there for decades with no one coming to repatriate them. They propose a plan to turn the old aircraft into a boat to sail back to civilization. This requires flipping the B-29 upside down, as this will be a more stable and watertight configuration. Bernadette needs to construct a sail for the boat, so the soldiers give her their battle flag of the Japanese Empire, which she uses as the primary fabric for the sail. She tells the soldiers that she will sew it in the top position as a symbol of respect.
Noah and Bernadette (or “Bernie”, as he calls her) fall in love after the two had resented each other at first. Bernie paints the name “Noah’s Ark” on the converted boat-plane. Dugan tells her that he does not like his first name, but as she starts to remove the paint, he says he is okay with it. The animals are also brought on board at Bobby’s insistence. Bernadette keeps a Bible close to her. After many days at sea, she tells Dugan that she has been inspired by the story of Noah’s ark in how a dove was sent to search for a sign of hope, so they decide to send their duck with a message attached, telling of their need for rescue. The duck flies westward, away from the direction of Hawaii, and hope dwindles. Bobby has been resentful of Dugan (since his first mistreatment of the animals), but the two eventually develop a close bond, especially after Dugan saves Bobby’s life when the boy falls overboard when they try to fish for food while a big shark is circling them. They are rescued by a United States Coast Guard cutter, which has the duck aboard, and the Ark is towed to Oahu.