The Dish pointed me to this touching video of a group of elephants in captivity saying goodbye to a dead baby. I highly recommend you read the entire post and it's links, but here's a taste:
...elephants, the only other known creatures that — whatever it may mean to them — purposely commemorate their dead, in a way [Coming of Age with Elephants author] Joyce Poole calls “eerie and deeply moving”: “It is their silence that is most unsettling. The only sound is the slow blowing of air out of their trunks as they investigate their dead companion. It’s as if even the birds have stopped singing.” Using their trunks and sensitive hind feet, the ones they use for waking up their babies, “they touch the body ever so gently, circling, hovering above, touching again, as if by doing so they are obtaining information that we, with our more limited senses, can never understand. Their movements are in slow motion, and then, in silence, they may cover the dead with leaves and branches.”
After burying the body in brush and dirt, family members may stay silently with it for over a day; or if a body is found unattended by elephants not related to it, they may pause and stand by for some time. They do this with any dead elephant, recently deceased or long departed with only the skeleton remaining. “It is probably the single strangest thing about them,” [Elephant Memories author] Cynthia Moss writes.