Battle of Zama

[Ibrahim]

1. As a cavalry screen, preventing the enemy's cavalry from going where it wants since horses are scared of elephants. (For an example of this, see the Battle of Ipsus)
2. As a front line hammer used right before the infantry engages in order to a) cause fright and b) disrupt an enemy's formation. When an elephant charges through a block of men, it creates a gap that one's own troops can then exploit.

The second way is how Hannibal intended to use them at Zama. That's why Scipio's deployment was especially useful. By breaking his troops up into smaller units with gaps between them, there's no formation for the elephants to run through and disrupt. After the elephant charge, Scipio reorganized the troops in the more standard Roman manner with larger maniples. It's not so much that Hannibal "wasted" elephants, as that Scipio countered especially well.

actually, that was only part of the story. remember, the elephants were poorly trained and inexperianced. It's also an observed fact that elephants do not charge ANY line of troops directly (that's why they were often rendered drunk-so they won't know better). and even if drunk, the elephant will still prefer the easier route, so they'll just travel through the gaps. hence why it was brilliant. the guy controlled not just Hannibal and his men's minds, but even the elephants

at least, so I've observedf about elephants, so I might be off.