The film opens as Alice Melbourne and Judson Ellis arrive at a California Municipal Airport by taxi. Alighting from the cab they tip the driver generously, bribing him to not say anything to anyone about them. Alice and Judson check the departure sign for The Silver Queen, heading for Panama City, Panama, and seem excited and anxious.
Also waiting for the same flight is Peggy Nolan, to whom a delivery of expensive flowers is made with a card thanking her for some favor. Peggy disdainfully tosses the card in the trash and gives the flowers to a woman selling cheap gardenias.
Soon after, the flight gets ready to leave and we are introduced to Professor and Mrs. Spengler, an elderly couple, and Joe, the flight's co-pilot, who is immediately attracted to Alice. Mrs. Spengler is a domineering woman, but her husband seems content to be bossed around like a child.
As they wait on the tarmac near the 'plane a car drives up and a well dressed man emerges with a young boy and another man. The boy is Tommy and he is being sent away with "Uncle" Pete until his father -- a mobster -- can follow later.
As the passengers board, Bill, the pilot, receives word that they will be transporting an anarchist back to Panama, but he assures the group there is nothing to worry about since the man will be in custody during the flight.
The prisoner is Vasquez, and is being accompanied by a bounty hunter named Crimp.
After Larry the steward helps everyone get settled, the flight departs with its twelve souls aboard. Bill and Joe discuss plans for the layover and Joe indicates he has an interest in Alice. He goes back to the passenger compartment where beds have been made up and people are turning in for the night -- except for Crimp who plans to stay up and make sure Vasquez doesn't "go for a walk" -- thus cheating the hangman and himself out of $5,000.
Pete tucks his young charge in for the night and helps him say his prayers (something Pete is unfamiliar with). Peggy comes up to the cockpit to visit with Bill, whose rudeness finally makes it clear that he wants nothing to do with her. When Alice rings for the steward, Joe takes the call and makes a play for her.
Next morning the 'plane arrives for a refueling stop in Mexico and the passengers have breakfast. Joe continues to pursue Alice, under the assumption that she is Judson's secretary. Peggy makes another stab at getting Bill to warm to her and is rebuffed again. Then Pete tells her that her help isn't needed when she tries to get Tommy to drink his milk. Peggy's been "marked" as a loose woman by her fellow travelers who want nothing to do with her.
Before boarding the 'plane a reporter confronts Judson and Alice and Joe learns that she is engaged to her "boss" and they are eloping.
As the flight continues and heads into stormy weather the Professor discusses the methods by which a South American tribe of headhunters practice their craft. The conversation is interrupted by a news bulletin which recounts how Tommy's father has been killed. Peggy again tries to help with Tommy, saying "he needs a woman." But Pete is still being judgemental and answers "he needs a lady." Mrs. Spengler intervenes and comforts Tommy.
As the storm they are flying through gets rougher, the passengers strap themselves into their seats and Crimp insists the pilots turn back. As the 'plane rocks back and forth a couple of metal cylinders break loose and crash through the back door. Tommy comes perilously close to going out the door when Llarry saves him and hands him to Pete. Just then the 'plane dips sharply and Larry is tossed out the door to his death. As Joe and Bill try to steady the 'plane Crimp tries to force them to turn back by waving his gun at them. In the struggle the gun goes off and is picked up by Vasquez.
With a damaged engine the Silver Queen crashes, and all eleven on board survive. The next morning Joe and Bill admit to the professor that they were blown off course and no one will know where they are. This is borne out by discussions at the airplane company headquarters as they discuss the missing 'plane.
The professor believes (based on vegetation at the crash site) that they are in a valley near the headwaters of the Amazon, and can only escape by flying out. Peggy approaches Bill with a cup of coffee and asks their chances, which he feels are "pretty slim." But he is at least warming up to her at this point.
The survivors gather around a camp fire and assignments are made which includes Mrs. Spengler being the group's cook. When she protests her husband's true mettle shows itself and he takes charge of their relationship again telling her not to argue, that she is the cook.
As Bill takes charge everyone except Crimp agrees with his role. At this point Vasquez gives Bill the gun he picked up during the flight, which closes the argument of who is in charge.
After gathering wood all day and working to clean out the 'plane the group listens to the news broadcast on the radio. They hear that the main search has been called off and there is little hope for them being found. Only Vasquez seems to take this news in his stride, since he was headed for execution at the end of the trip.
The next days shows some of the passengers bonding, including Pete and the Professor. Later that night Bill explains to Pete that he expects Pete to stand guard with him and Joe, which is why he allowed Pete to keep his gun. Judson gets drunk that night and his true nature begins to show. When he gets into the 'plane and disturbs people's sleep, Peggy goes outside and talks with Bill, who tells her about the death of his wife. This breaks the ice between Peggy and Bill even further.
Days pass as Bill and Joe work on fixing the broken 'plane and the group starts to clear a runway for their takeoff. Further bonding occurs between Vasquez and the Spenglers, and even Peggy and her fellow passengers. Only Judson's drinking and Crimp's bad attitude prevent an atmosphere of cooperation from prevailing. FInally Alice begins to see that her infatuation with Judson has ended as she grows fonder of Joe.
About three weeks after the crash Crimp and Judson have a fistfight over liquor and Crimp disappears. That night around the campfire Judson brings up the possibility of Indians, scaring little Tommy and raising the ire of Pete and the others. Bill announces they plan to try and fly out in the morning. Later the professor tells Bill and Joe he thought he heard drums, a fact they plan to keep to themselves.
The next day they try to get the engines running, and have success. Flushed with the excitement of imminent escape the group rushes to finish the runway and lighten the 'plane. During the work Tommy supplies water for the workers, but wanders off into the jungle. Looking for him Pete and Peggy follow his trail and find him not far off. They also find Crimp's body, with a posion arrow sticking out of it. Pete insists Peggy take Tommy to camp and he stays behind guarding their retreat. As the group prepares to take off Peggy returns with Tommy, followed by a staggering Pete, who falls at their feet with arrows in his back and dies.
The rest rush into the 'plane and prepare for takeoff. But the 'plane's oil lines break, needing more repairs. The Professor tells everyone that they are safe until the distant drums they hear stop.
Unable to repair one of the engines fully, Bill and Joe explain to the group that the 'plane can only carry 5 people, one being Tommy. As they discuss who deserves to be saved, Vasquez takes the gun and tells them he will decide who goes. He says he will stay since he was going to be executed anyway.
Vasquez is approached by the Spenglers, who agree that they must not be chosen to leave. They feel like they have reconnected during the crisis and they ask Vasquez to leave them behind and send the young people out.
Faced with being separated Alice and Joe hint about how they feel about each other. Peggy and Bill have a similar conversation, and Bill tells her he has money set aside she can use to raise Tommy. Judson tries to bribe Vasquez to choose him.
As Bill gets the engines revved up, Vasquez announces his choices: Bill, Tommy, Alice, Joe and Peggy. Judson is incensed and attacks Joe and Vasquez, who shoots him. The rest get on the 'plane and prepare to fly out.
As the 'plane lifts off, the Professor and Vasquez discuss their fate. They know being taken alive would involve torture and Vasquez agrees to shoot the Spenglers to spare them that. He says he has three bullets left, but actually only has two, leaving him alive to be captured by the headhunters.
As the Indians creep closer to Vasquez, the camera pans up to a shot of the Silver Queen flying over the treetops back to safety.