When Bart wins a KBBL radio contest, deejays Bill and Marty give him the choice of two prizes: $10,000 in cash or a full-grown African elephant. Bart chooses the elephant. Never thinking that anyone would choose the gag gift, Bill and Marty are caught off guard. They offer Bart a variety of other prizes, all of which he refuses. Their jobs at stake, they arrange a delivery of a full-grown elephant to the Simpsons' house.

Bart names the elephant Stampy and ties him to a post in the backyard. Lisa thinks that keeping the animal away from the jungle is cruel, while Homer is concerned that the pachyderm is eating him out of house and home. To help offset food costs, Bart offers rides on Stampy for $2.00 apiece, but Homer decides that Stampy's upkeep is too high and sells the elephant to an ivory dealer. Before the dealer can claim him, Bart sets Stampy free.

Stamp blazes a trail of destruction throught the town. Bart insists that Homer give him to an animal refuge, but Homer does not want to lose thousands of dollars from the ivory dealer. Homer gets stuck in the tar pits, and is in danger of sinking, when Stampy pulls him out. Grateful to Stampy for saving his life, Homer gives the elephant to an animal refuge.