Penniless but full of ideas, Steve Martin and Johnny Gambi, engineers who served in the Navy during World War II, walk down a quiet road on the gulf coast of Louisiana. Teche Bossier, owner of the Port Felicity Fish Co., agrees to drive them into the shrimping town Port Felicity for five dollars. On reaching their destination, Gambi rents a shrimp boat from Dominique Rigaud, though the fisherman's daughter Stella Rigaud distrusts them immediately.
Gambi and Steve use the boat to show potential investor, and the plan’s backbone, an offshore drilling idea that could transform their fortunes. Claiming that he has designed a drilling platform that can withstand any storm, Steve estimates that by investing one million dollars now they will soon tap an oil reserve worth two billion. His enthusiasm is infectious, and the investor agrees to fund the project, albeit with a strict three-month deadline: if oil isn’t found, the venture will be abandoned and the men will be out of work.
Several weeks later, Gambi meets and falls for Francesca Rigaud, who is betrothed since childhood to Philippe Bayard. After singing a love song in the local gathering place Bon Chance, Philippe is upset to see Francesca enter with Gambi. Teche, who good-naturedly calls the oilmen foreigners, agrees to help Steve and Gambi, but Stella Rigaud refuses to accept Steve’s claim that oil will be good for the town. Nevertheless, the outsiders hire a crew and begin their search for oil.
When Teche sees dynamite charges being dropped into the gulf, he begs them to stop, believing that the explosions will kill the shrimp and worsen an already dismal shrimping season. Steve maintains that the charges are safe, but Teche returns to town and incites the fishermen to form an angry mob. Fortunio Bonanova as the sheriff arrests the oilmen and Francesca angrily denounces all the men. Steve manages to scare the mob away by exploding sticks of dynamite behind them, and he placates Stella by warning Gambi to stay away from Francesca. Steve gently advises Francesca to “go back to [her] people.”
With one month gone, Steve drives the building crew relentlessly, and the platform and rig are completed on schedule. He immediately orders the drilling crew to get started, and the exhausted Gambi is relieved when a hurricane warning gives the men an excuse to take the night off. Gambi and his men enter the Bon Chance with Francesca, and Philippe furiously punches his rival and starts a brawl. The sheriff, Fortunio Bonanova, arrests the oilmen and Francesca angrily denounces all the men.
During the storm Stella visits Steve at the rig, determined to have Gambi fired so that he stops seeing her sister. Steve explains to the group that, if he could pull up a resource that has been in the earth for millions of years, then he will truly have accomplished something. Stella finally abandons her suspicion and kisses Steve, but back in town Philippe persuades Teche to help him destroy the oil rig. With the hurricane winds rising, Philippe climbs onto the platform and lights a bundle of dynamite, but Steve sees him and the two men fight. Philippe trips and disappears under the waves, and Steve, horrified, assumes that Stella was involved in Philippe's plot.
The rig survives the storm, and in the morning drilling begins. However, eight days before the deadline, MacDonough visits Steve and sadly delivers the news that the board of his company has voted to stop the drilling operation the following day, fearing a penalty for non-payment on their lease. MacDonough has already spent all of his own money, and the crew is unable to work for no pay. Gambi soon returns from town, announcing that he has just married Francesca. Steve punches Gambi, who in reply loudly chastises Steve for having driven him and the men too hard. Steve orders them all to leave, intending to do the drilling himself, whereupon Gambi hesitates and then persuades the crew to remain. While the men are drilling, they discover that the troublesome shrimp that have been clogging the valves are actually the huge golden shrimp that have so long eluded the local fishermen.
Steve later takes Francesca to the rig, infuriating Dominique, who inflames the fishermen by declaring that the oilmen will steal their daughters and destroy the town. At Stella's request, Teche go to warn Steve about the impending mob on its way to the rig. There, Steve feigns ignorance about the golden shrimp and asks Teche if he can help him get rid of the creatures. He then addresses the furious mob to assure the men on their concerns: Francesca's marriage is a happy one and, moreover, oil will bring progress and prosperity to Port Felicity. Despite these words the mob decides to destroy the structure, but at that moment oil explodes through the rig and onto the platform. Later, the fishermen discover that the golden shrimp bed is huge, and consequently the conflict between the oilmen and the fishermen is resolved. Teche Bossier then convinces Steve that Stella was not involved in Philippe’s plot and the lovers finally come together.
