IMF leader Dan Briggs goes to a curio store and asks the manager for the rare recording. The manager gives Dan a record and leaves, and Dan removes the disk from its hermetic seal. He then plays it on the record player in the office, and a man's voice welcomes Dan back. It then tells him that General Rio Dominguez, the ruler of Santa Costa, has received two nuclear warheads from a foreign power hostile to the U.S. The warheads are stored in the vault of the Hotel Nationale where Dominguez has his headquarters. The general, who hates the U.S., plans to use them. Dan must steal the warheads and bring them to the U.S., an "impossible mission" if he chooses to accept. The record then self-destructs after a minute's exposure to air.
Later, Dan goes to his apartment and goes through photos of prospective team members. For the mission he selects actor, magician and disguise artist Rollin Hand; safecracker Terry Targo; electrical engineer Barney Collier; fashion model Cinnamon Carter; and strongman Willy Armitage.
The team meets in Dan's apartment and plays penny-ante poker while waiting for their leader. Rollin tries to steal the pot via sleight of hand and Terry catches him at it, while Cinnamon and Barney display the same card. As Rollin steals the deck, Dan arrives and begins the briefing. Rollin warns that he can't impersonate Dominguez on television during his upcoming speech, and Dan assures him that Barney will sabotage the broadcast. Barney confirms that he'll rig the fireworks display on the day of the transmission but he'll need a day to set it up, and Dan assures him that he'll get the time. Terry warns that the warheads are wired into the locks of the case that they're held in, and one wrong move will set them off. Dan is sure he can get the codes from Dominguez, and points out that the vault was intended to keep people out, not in. Willy assures his teammates that he can lift the combined weight of the warheads, while Cinnamon says that her job is easy because she'll only be doing what comes naturally.
The team goes to Santa Cost and Willy drives Dan in. They stop at the side of the road as a military convoy drives by. Barney is in a separate van posing as an exterminator, using a tool box with a hidden compartment containing electronic gear. Dan and Willy arrive at the hotel and Dan explains to the soldier on guard that he's a Swiss clock salesman and Willy is his manservant. The soldier lets them into the hotel and Willy effortlessly carries Dan's two large cases. When they check in, Dan asks about the vault and the clerk tells him that the time lock will let them open it in ten minutes. Cinnamon and Rollin come in behind them as a husband and wife, with Rollin confined to a wheelchair.
Dan and Willy take the cases to the vault and the clerk on duty takes Dan's fingerprint as a security measure. He assures them that no one can open the vault until 11 a.m. that evening, in 12 hours. Colonel Alisio and his men arrive to guard the vault as Willy carries in the two cases. He puts them down and leaves, and Alisio closes the vault. Once the vault is sealed, Terry emerges from one of the cases, using a rebreather for extra air, and begins examining the case holding the warheads.
Dan and Willy go back to the lobby and Cinnamon creates a distraction by dropping her purse. The IMF leader tells her that Terry is in place and they'll make the switch that night. Meanwhile, Rollin releases mice from a case and people react in disgust and horror. Dan and Cinnamon put transmitters on the phone while the clerk is distracted. He calls for an exterminator and Cinnamon intercepts the call on the house phone and redirects it to Barney, who says that he'll be there soon.
Terry goes to work in the vault, examining the door lock from inside. Meanwhile, Cinnamon and Rollin go to their room and Rollin removes is old man disguise. He then reviews newsreels of Dominguez and practices the general's mannerisms.
Barney arrives at the hotel and tells Alisio that he needs permission to go through the entire hotel since the rats could be anywhere. Alisio agrees.
At dinner that night, Dan and Willy eat in the dining room and watch while a camera crew sets for the general's broadcast the next day. Meanwhile, Barney has crawled into the air shaft above the dining room and sets up his jamming equipment. Cinnamon is dining alone and tells the waiter that her husband is too ill to join her, and Rollin continues to master his impersonation.
Just before 11 p.m., Terry finishes his work and gets back in the case with his equipment. Dan and Willy go to the vault and remove the cases, and tell the night clerk that they'll bring them back in the morning. Once they're back in their room, they let Terry out and he tells them that he can open the vault door but will have to blow the timelock.
Cinnamon goes back to her hotel room and helps Rollin prepare his Dominguez disguise. Once he's ready, Cinnamon takes Rollin to the lobby in the wheelchair with his face covered by his broad-brimmed hat. She then draws the soldiers' attention long enough for Rollin to discard the hat and get out of the wheelchair, and tell them to focus on their job. Dan and Willy arrive and Rollin tells the soldiers to let them through for their appointment with him. As Rollin goes, he tells the soldiers to bring Cinnamon to his room in 10 minutes. Well aware that Dominguez is a womanizer, the soldiers smile knowingly.
Rollin, Dan, and Willy go to the door to Dominguez' suite and take out the two soldiers guarding the door. They release Terry from the case and he starts to pick the lock to the door. However, Dominguez comes out suddenly and sees the disguised Rollin, surprising them. Terry instinctively tries to stop Dominguez from slamming the door shut. The safecracker succeeds, but the door slams on his fingers. Dan and Willy take out Dominguez and get the general and Terry inside, while Rollin closes the door and confronts Alisio and his men as they arrive to investigate the commotion. Rollin tells them that the two soldiers guarding the door have disappeared and tells Alisio to find them while he works on his speech. He goes inside and Terry reveals that his hands are broken.
Barney moves around the hotel, claiming to look for vermin but actually tampering with the cameras. Meanwhile, Dan bandages Terry's hands. When Rollin wonders how they can get the vault open, Dan assures him that he has a plan. A solider escorts Cinnamon to the room and Rollin brings her inside and closes the door. Thinking quickly, Dan tells Cinnamon to wait an hour and then flirt with the vault clerk and get a blank signature card. He then tells the team that he'll go into the vault instead of Terry, and that Rollin will impersonate him to get the cases out.
Barney finishes planting his jamming equipment and goes back to the air shaft. Meanwhile, Rollin flirtingly suggests that Cinnamon help him perfect his role but she tells him that they'll stick to working on the speech.
Back in their room, Dan and Willy remove Terry from one case and the captive Dominguez from the other. Meanwhile, Alisio comes back to see Dominguez. Rollin makes sure that he stays outside and Alisio reports that they've been unable to find the two missing soldiers. However, he assures his ruler that the men are loyal. When Alisio starts to discuss the briefing they had that morning, Rollin tries to bluff it out. Cinnamon provides a vital distraction by coming out of the bedroom in nothing but a towel. Alisio also knows that Dominguez is a womanizer and apologizes for interrupting.
Dan tells Dominguez that they're going to be spending some together. Terry warns that given how much larger Dan is than he, there may not be enough room for enough oxygen tanks to keep him alive for 12 hours.
Cinnamon flirts with the vault guard and steals a blank signature card, and then slips it beneath the door to Dan's hotel room. Dan puts his fingerprints on it and slips it back out to Cinnamon.
The next morning at 11 a.m., Willy puts the cases into the vault. He's alone and the vault clerk tells him that only Dan can withdraw them. Once the vault door is closed, Dan emerges from one case and removes Dominguez from the other. When the general yells for help, Dan tells him to conserve his air.
As the day passes, Barney plants the fireworks and Rollin rehearses his Dominguez impersonation. Inside the vault, Dan follows Terry's instructions while the general watches him. Dominguez insists that he won't use the warheads within the U.S., and Dan makes him the same promise: the warheads won't explode in Dan's country. Once he has planted the magnetic device, Dan examines the case, which has three 10-color wheels that have to be set in a specific sequence.
Alisio comes to see Rollin and tells him that they're ready for the televised speech in 20 minutes. Rollin, who has been working on his Dan mask to get back to the vault, tells Alisio to come back in 10 minutes. He forgets that he left a Dan mask in the wastebasket. When Alisio comes back, Rollin goes to the dining room. He prepares to give his speech and Barney jams the transmission.
A panicky Dominguez accuses Dan of insanity. The IMF leader, undeterred, says that he's going to dial Santa Costa's national colors of red, green, and white. He starts to dial and Dominguez cracks, telling him that the colors are red, white... and blue. Amused at Dominguez's sense of irony, Dan successfully opens the case and sighs in relief.
Rollin storms off while the technicians try to restore the cameras. Alisio goes after him, insisting that something is wrong. Rollin tells him not to bother him until he has something definite and goes to his room. Meanwhile, Cinnamon has disguised Terry as her husband and takes him out in the wheelchair.
In the general's suite, Rollin orders the soldiers to go to the lobby and then starts removing his disguise. Alisio decides to come in and sees the discarded mask in the wastebasket. Rollin comes out and knocks the officer out before he can sound the alarm.
Barney returns to his vault while Rollin, now disguised as Dan, goes with Willy to the vault. Cinnamon is there and switches signature cards so that the guard unwittingly signs the card with Rollin's fingerprints on Dan's card. She puts in her jewelry case while Willy removes the two sample cases. Once the door is sealed, Dan emerges from the bomb case where he hid with Dominguez.
Cinnamon and Terry go out through the lobby and get in their ambulance, while Willy and Rollin, still disguised as Dan, go to Dan's car. Barney sets off the fireworks, which both distract the soldiers and make enough noise to cover the explosion as Dan blows the timelock from the inside. He knocks out the clerk and heads through the lobby, but the front desk clerk sees him and realizes something is wrong since he saw Rollin-as-Dan a few minutes earlier. Realizing something is wrong, the clerk calls the military.
Outside, Dan gets in the exterminator van with Barney and they head for the rendezvous spot on the highway. Meanwhile, Cinnamon and Terry force the clerk at gunpoint to drive them.
As the soldiers call the border station, the three cars crash through the barrier. Dan shots one guard aiming at them from a watchtower and then activates a smoke cannon in the back of the van. When the soldiers follow them in jeeps, they go off the road due to the smoke and hit the abandoned exterminator van. Dan and Barney have transferred to the ambulance, and drive after Rollin and Willy. They get into a private plane with the warheads and take off just ahead of the guards, leaving nothing behind but Rollin's discarded Dan mask.