In the film, Francis Robinson, the youngest of the family, finds a young baby elephant in the jungle all by itself. After the dogs, Duke and Turk, save him and Francis from the tiger on the island, Mother Robinson allows Francis to keep the baby elephant, who is later proven very instrumental in helping the family build their treehouse, and names him Rocky. Rocky, with Francis' new pet monkey on his back, even helps the two older Robinson boys pull their sailboat to the water so as to allow them to find a way off the island.
On the day of the Robinsons' new holiday, Rocky is one of the animals who participate in the race, with Francis riding him, along with Turk (ridden by Francis' monkey), Lightning the donkey (ridden by Fritz), Clementine the ostrich (ridden by Ernst), and Duchess the zebra (ridden by Roberta).
In the end, after the pirates' deaths, and as Ernst travels to London with Roberta's grandfather, Captain Moreland to continue his education there, Rocky can be seen running away along with Clementine, the dogs, and Duchess as Francis tries to bring them back.
Rocky is the real name of the elephant who played him in the movie. According to Kevin Corcoran, who played Francis Robinson, Rocky got his name due to the fact that he never stood and rocked back and forth all the time. Corcoran got to be friends with and play with Rocky off camera, and he remembered Rocky was very friendly to him.
It is unknown what happened to Rocky's herd in the movie. An older elephant, which presumably would have been a parent to Rocky, was brought to Tobago for the film's production, but did not make it into the final film.