Torlonia Collection.Tale of the Elephant Quadriga. This is a gold coin from the reign of Nero, c. 55 AD, showing Claudius and Augustus riding in an elephant quadriga.
The clearest textual evidence for such behavior comes from Plutarch's Life of Pompey. Plutarch tells us that in 89 BC the young Pompey
tried to ride into the city on a chariot drawn by four elephants; for he had brought many from Africa which he had captured from its kings. But the gate of the city was too narrow, and he therefore gave up the attempt and changed over to his horses.I have to say that this does not strike me as an especially reliable source. Pompey was at that point too young to legally celebrate a Triumph, and had been neither a Praetor nor of Consul, so his demand for this honor no doubt struck many older Romans as presumptuous. They would have been looking for reasons to mock him. Note that since he never actually appeared in an elephant-drawn chariot, nobody saw this, so the source would have to have been someone very close to Pompey. Plus, the morality tale is too perfect. In SPQR, Mary Beard is very coy, and never says if she believes this or not.
So far as I can tell, neither Tacitus nor Suetonius ever mentioned emperors being drawn by elephants, and that strikes me as the sort of thing they would have very much enjoyed. If Nero or Caligula had ever ridden in a chariot drawn by elephants, surely some one would have told us?
I should emphasize that I am not saying this is impossible; after all elephants certainly can be trained to pull carts. The Romans had plenty of elephants, especially during the late Republic. There are several coins from the Hellenistic kingdoms (above, Seleukos I) that show kings this way, and they really did use elephants on a large scale, so who knows what they got up to. But the formula of the Roman Triumph was very firmly set by tradition, and it specified horses, so I think anyone who wants to argue that some particular Roman actually was pulled by elephants has to prove the case.
was surmounted by a statue depicting Emperor Theodosius in an elephant Quadriga. Byzantine Historian George Kedrenos tells us that this is an accurate depiction of Theodosius entering the city. However, he was writing around 1050 AD and is not considered very reliable about events that far in the past. Also a very weak source, I would say.
On the other had, we do have a story about Dionysus entering India in a chariot drawn by elephants, and several depictions of other gods and goddesses in this wise.
This coin of Domitian probably depicts the Arch of Titus in Rome; Titus was Domitian's brother and Domitian set up the arch c. AD 81 to celebrate his brother's achievements. You can see that in this depiction the arch has an elephant quadriga on top. But there is also a very fine sculptural relief on the arch showing Titus' Triumph, and there he is clearly shown being drawn by horses. I think this pretty clearly marks the distinction between the living man and his divinity.