I saw this on TV long, long ago. It was B&W, probably 50s or 60s. Due to the presence of elephants, I assume it could have been set in India or Africa. Anyway, the plot had to do with elephants rampaging for no good reason. Some people set off on an expedition to discover what was causing the elephants to go crazy. Turns out it was mammoths! Yes. Mammoths. The Mammoths were bullying the regular elephants and making them flee in terror, hence the rampages and stampedes.
You've got me very curious about this one.
Could it have been an episode of Science Fiction Theatre called "Dead Storage?"
http://www.imdb.com/title/tt0696270/ (http://www.imdb.com/title/tt0696270/)
Actually, it's THE JUNGLE (1952).
http://www.imdb.com/title/tt0044778/ (http://www.imdb.com/title/tt0044778/)
Looks like. Move to solved!