Elephants were sometimes armoured, and often not armoured. This is similar to the case for warhorses. Indeed, the armour for elephants has much in common with that for horses, owing to their approximately similar shape as quadrupedal animals: body armour to cover the sides and back, usually draped over the back, forehead protectors, and protectors for the front of the body. To these elements common to both horse and elephant armours, one can add trunk protectors and large (while some horse armours include ear protection, elephant ear protectors are much larger).
It isn't obvious when elephant armour became common, but it appears to have been used already in the late 1st millennium BC, at least in India. Most surviving examples are textile, metal, or textile + metal. According to Pant (1997), leather was used in the late 1st millennium BC (but note that this, as with many references to "leather" armour, might refer to rawhide armour).
An example of a fairly minimal textile armour, covering the face and back and sides of the body:
Textile armours were also used as parade armours. Whether these parade armours were of sufficient thickness for battle I don't know. Here is an example from the Delhi Durbar celebrating the coronation of Edward VII as Emperor of India in 1903:
One of the best-known metal armours is the example from the Royal Armouries:
It's mail-and-plate (i.e., small plates joined together by riveted mail). It's missing two of the 3 panels on the right hand side; if these were present, it would probably weight 155-160kg.
This example from art appears to show metal armour (compare the colour with that of the armoured soldiers):
This armour is possibly scale, with small plates attached to a textile backing. For a similar example,
which AFAIK is from a museum in India. I don't know any details about this armour (such as authenticity, age, whether it's for parade or battle).
Plate armours were also used:
(again, from a museum in India, details unknown). Trunk armour like this was certainly used (Pant, 1997).
A plate head-and-trunk protector (with large plates joined by mail):
As for weapons, the elephant often has none beyond its natural weapons of feet, tusks, and trunk (and great size and weight). Again, just as the case for warhorses, it is the rider that carries and used the weapons. The elephant riders could either sit on the back of the elephant, or on a howdah, a tower or platform carried on the back of the elephant. From their high perch, they might use javelins, bows and arrows, or guns, or use long spears. Elephant drivers, usually sitting on the elephant's neck were often essentially unarmed, with their elephant goad ready as an emergency weapon. Some SE Asian elephant drivers used a combination elephant goad-glaive weapon.
Sometimes, elephants were equipped with weapons. One example are "elephant swords", worn by the elephant on its tusks:
Spikes were sometimes attached to the armour, which could perhaps serve as weapons. Artwork sometimes shows elephants wielding weapons with their trunk, including what look like conventional swords as used by humans.
This armoured elephant already shown above:
is also equipped with weapons: note the flail held in or attached to its trunk.
Reference:
G. N. Pant, Horse & elephant armour, Agam Kala Prakashan, 1997
