[Saurreg]

The only recorded persons who successfully countered elephants in battles were Alexander and Scipio Africanus.

Alexander's heavy infantry, the phalangites would poke at the animals eyes, slash the softer under bellies or the genitals with their 14 foot long sarissas after they have killed the riders. In any case the macedonians suffered heavily in that battle.

Scipio made use of a large number of horns and trumpets to scare the Carthaginian elephants. This caused them to bolt back into the carthaginian ranks, crushing their own men.

There were other reasonings in both cases that the soldiers parted ranks to allow the elephants to pass through them. But it the poking and slashing drove the elephants into a frenzy, it would have caused more damage.

Horses are terrified of elephants. So the part where highly skilled Rohirrim horsemen darted between the legs of the mumakil would not have worked.

In the case of the Mumakil, may I suggest this sensible tactical doctrine:

Tactics 101: Countering the Mumakil

At first sight of a mumak;

1. Say a prayer to whatever higher power you believe in.

2. Turn to a direction perpendicular to the beast's line of travel

3. Run like hell.

The fact is, Tolkien's elephants were so big that I don't think anything on the battles of antiquity could have stop that, save for a highly accurate and lucky shot from a siege artillery. Then again, I doubt that in this newtonian world, the mumak's legs would have been strong enough to support it's body without snapping. Ditto for the internal organs which would be crushed by the beast's bulk.