Kyle's elephant appeared in the episode "An Elephant Makes Love to a Pig". The boys made a bet that they could create a pot-bellied elephant (an elephant crossed with a pot-bellied big) before Terrance Mephesto and his friends could clone a whole human being for the science fair.
With some help from Chef and Elton John, they eventually succeeded in getting Cartman's pot-bellied pig, Fluffy, and Kyle's elephant in the mood to make sweet loving. However, on the day when they were supposed to show their project, Fluffy had yet to give birth. Fortunately, Fluffy gave birth to a piglet with Mr. Garrison's face just in time, winning the competition.
Fluffy appeared again in "Cherokee Hair Tampons", but neither the elephant nor the piglet have made any subsequent appearances. He does appear in pictures, like in "Mecha-Streisand" and "Ike's Wee Wee".