The act of draping one's limp penis over the shoulder of an unsuspecting victim from behind. The recipient of the "Caterpillar" is usually sitting down and the actor standing up. There have been known incidences of the "Caterpillar" to have been given to someone standing erect by somebody much, much larger than them. This method is also achieved more easily at an arena or stadium with tiered seating.
Oooh shit! You've got a Mississippi Caterpillar on your shoulder!