If we're speaking of an African Elephant, then that species most likely lives in a "Tropical Savanna". Some say the desert, but you rarely see an elephant trekking through sand dunes. We are studying biomes in Environmental Science and I've yet to ask our teacher, however, I've done a little bit of studying on my own and came to the conclusion that elephants do in fact live in the Tropical Savanna, at least the ones who aren't trekking through the desert.