Dealing with Non-cavalry Mounted Opponents
The Romans tended not to use chariots in combat, because they were only useful on completely flat ground. When the army faced opponents who used them, they simply set up obstacles that would severely damage or destroy any chariot foolish enough to try and cross them.
The Roman army had several ways of dealing with mounted pachyderms. Elephants usually carried several riders, the idea being that the riders could finish off any attackers before they had enough time to kill the elephant. The first method was to pick off the riders with archers, which could be difficult if the riders themselves were archers, because they had a height advantage. The second was to have the cavalry ride in circles around it and throw javelins. Another tactic was to part ranks in front of the elephant, and then rush in and attack its flanks.