One of the most effective ways to kill an elephant unit is to a) get them to rout (throwing a bunch of units at an isolated unit usually does the trick), then b) send cav after them.

The normally nearly indestructable elephants die about as quick as any other unit when routing from pursuing cavalry.


On a related note, I remember once having a unit of skirmishers chased by a unit of elephants. The elephants had caught up with my guys, so I told them to withdraw in an attempt to save them. After about five minutes, I noticed that my guys hadn't taken any casualties. On a hunch, I turned off their withdraw orders. Sure enough, my guys started dying. Then I put them back on withdraw. The dying stopped. In all cases, the elephants were in direct contact with my unit. But as long as my guys were withdrawing, they were invulnerable. Strange.