Elephant's Graveyard begins with the introduction of the circus and all of it's members speaking of their roles in the circus. We are also introduced to the townspeople of Erwin, Tennessee. The circus has just come front Kingsport where the townies were thrilled with the circus and its main attraction, Mary, a five ton elephant. In Kingsport a 25 year old, red-headed man asks to join the Tour Manager's circus to work with Mary. He's given a job cleaning up her feces, and when they arrive in the next town, Erwin, Tennessee he wants to ride Mary through Main Street during the welcoming parade. The Trainer objects to this as the young man is too new, but the Tour Manager demands the Trainer allow it to be.
The townies from Erwin all arrive early to claim their place on the street to welcome the circus. And Red, the newbie, rides Mary through the crowd. But, the animal sees a watermelon rind that normally would have been eaten by the pigs which eat the town's slop thrown into the street; the pigs have been driven away because they are not accustomed to so many people being on the main street. Mary goes for the watermelon rind and when she does the young man, Red, atop her attempts to pull her back multiple times. So, Mary takes the man off of her with her trunk and throws him into a vending machine, then walks over to him and steps down on his head until she crushes him to death. Mary then goes about eating the watermelon.
The town's people are enraged and attempt to shoot Mary, but the bullets do nothing. The circus team leads Mary away and the Marshall agrees to deal with Mary later. The Tour Manager allows the circus show to go on and the Ballet Dancer attempts to show how gentle Mary actually is, but the town wants blood and won't settle for less. That is, everyone except for the Preacher, who doesn't want the animal to be killed. The townies ignore his plea and they decide that hanging the elephant will satisfy everyone's need for vengeance.
The night before everyone prepares food to bring to the hanging the next day. The Trainer gets the chain around Mary's neck and the crane begins to pull her up off her front feet, but gets stuck because they forgot to unchain Mary's leg from the railroad track and her leg is broken open. Then, the chain around her neck breaks and she comes crashing down. Another chain is wrapped around her neck and she is hung until she is dead.
The final sequence of the play has all of the characters from the circus and the town revealing the horror they imposed in the name of justice. We even listen in as the Marshal lauds what they have done as belonging to the American Dream, that anything can be done in America. The Clown weeps for Mary as he digs her grave with a shovel and refuses to allow the Steamshovel Operator to dig for him. The Hungry Townsperson speaks of the memories elephants have, that they don't forget people do, like the people of Erwin who have already forgotten the black boys they hung in their very city. He says that elephant's memories must be so good because of all the peanuts they eat. He offers the audience peanuts and leaves. The Preacher speaks of how the church will finally be full this weekend, and The Ringmaster speaks of digging up Mary to remove her tusks. Money needs to be made back. Mary cost the circus $8,000 and they must get any return.
