Do elephants show caring behavior

Some people think they do. Some would say that an elephant has such a small eye for its size that it needs to clean it often. The elephant seems to cry because its eyes are constantly cleaned by the tear duct.

They are one of the most socially, and emotionally complex creatures on earth. Elephants grieve and feel sorrow just like people. I'm not sure if they cry, you could be thinking of the secretion around the males eyes, when in must, or like the above answer states, cleaning of its eyes.