Elephants represent sensuality as well as strength across Asia. In olden days, in India, people use to measure their strength in elephant's power, as people of today measure the power by horse - horsepower. Bheem one of the Paandav, Keechak who misbehaved with Draupadee in Viraat Nagar, Jaraasandh, Dwivid (monkey, the helper of Raam), Pradyumn (Krishn's son) and Paurav who was killed by Arjun in MBH war - all had 10,000 elephants' power.

Elephant also represents Jupiter in Hindu astrology (Jupiter being the planet for all kinds of expandability)
Elephants always do Abhishek Vishnu's consort Lakshmee Jee.
Even one of our gods Ganesh Jee has the head of an elephant.

(1) Indra's Elephant Airaavat
Stories such as these clearly indicate that in South East Asia in general and in India in special, elephants are associated with rain and fertility. In Puree, Udeesaa, at the height of summer, the presiding deity Jagannaath Jee, is bedecked with a mask of an elephant in the hope that it will serve as a talisman and bring in monsoons sooner.

Little wonder then that Indra, King of the Gods and God of the Sky, is visualized as riding an elephant. Not the ordinary elephant, but an elephant with white skin, six trunks and six pairs of tusks called Airaavat. Indra rides atop Airaavat into battle and hurls his thunderbolt at dark rain-bearing monsoon clouds, visualized as a herd of dark elephants, forcing them to release rain so that the red earth can turn green.

Amongst Airaavat's many titles are names such as 'the wandering cloud' 'the brother of Sun' leaving no doubt that Indra's white elephant is symbolized as the white clouds that embellish the sky when the rain clouds have passed.

(2) Elephants Did Abhishek of Lakshmee Jee
Eight elephants from the cardinal and ordinal directions came together to welcome Lakshmee, the goddess of wealth, when she rose from the ocean of milk.

(3) Shiv and Elephant Skin
Elephant skin cannot be tanned easily. Thus it rots. Shiv by wearing it reinforces his role as one who holds all things material in disdain. Shiv Jee killed Gajaasur, wore his skin and danced with joy. (see (6) Gajaasur below)

(4) Gajendra
In Bhaagvat Puraan, 8/2 Vishnu rescues the king of elephants, Gajendra, from the jaws of a crocodile. The king of elephants surrounded by cow-elephants is a metaphor for the sensual delights of the world, the crocodile representing the bondage of materialism. Liberation comes when the elephant (sexual power) raises its trunk and offers a lotus (devotion) to the Lord to be liberated from the bondage of materialism.

(5) Four Gajapati
Four Gajapati in four directions : Custodians of the planetary systems of the universe..
tad-uparishtac catasrishv asasvatma-yoninakhi la-jagad- gurunadhinivesit a ye dwirada-pataya rishabhah pushkaracudo vawmano 'parajit iti sakal Lok stithi-hetavah

On the top of Lokaalok mountain are the four Gaja-pati, the best of elephants, which were established in the four directions by Brahmaa Jee, the supreme spiritual master of the entire universe. The names of those elephants are Rishabh, Pushkaraachood, Vaaman and Aparaajit. They are responsible for maintaining the planetary systems of the universe.

Lokaalok is situated one billion miles from the edge of the universe. Naaraayan, expanding His opulence, resides upon this mountain.

(6) Gajaasur
There was an elephant-headed demon too - Gajaasur, who terrorized the world, a metaphor for the dangers of sensual pursuits undoubtedly. Shiv Jee killed him on the request of Paarvatee Jee.

In Tibetan Buddhist art, one often comes across images of Mahaakaal (another name of Shiv) standing upon an elephant-headed demon. Some believe that he is Gajaasur, the demon of materialism; while others say that the elephant-headed demon represents proto-Ganesh; because long before Ganesh became the much-loved god who removes obstacles, he was a much-feared god who created obstacles. This tradition still exists in remote Tibet where the elephant-headed deity is feared and needs to be trampled by the Lord of Time, Mahaakaal.

But as Hinduism evolved in India, the elephant-headed demon destroyed by the Lord of Time became the elephant-headed son created by Shiv. Why did Shiv use an elephant's head to resurrect the son autonomously created by his consort, the goddess Shakti?

The instruction given to his attendants was: "Go to North and fetch the head of the first living thing you come across." North is the direction of growth in Vaastu and according to Brahm Vaivart Puraan, the creature first seen by Shiv's attendants was the white Airaavat, the mount of Indra.

Clearly, the killer of elephants is creating his son using the ultimate symbol of material splendor. After creating the elephant-headed Ganesh, Shiv stops being the world-renouncing hermit and transforms into Shankar, the world-affirming householder. Thus the elephant brings with it life and growth, wherever it goes.

If elephants represent wealth and power and material grandeur, then they should not matter to ascetics. And they don't. Shiv, the supreme ascetic, is called Gajaantak (Gaj + Ant), he who killed an elephant, flayed it alive and used its thick skin (the Gaja Charm) as a cloak.

(7) Gajmukhaasur
There is another Asur, besides Gajaasur, whose name was Gajmukhaasur - means whose head was of an elephant. According to one version Gsnesh Jee turned him into a mouse and made him as his ride.

(8) Food for Garud Jee
His another reference is in context of Garud Jee. As soon as Garud Jee was born, he decided to free his mother Vinataa from the slavery of her sister. He had to bring Amrit for that. As he felt hungry, he asked his mother something to eat. Seeing his body, Vinataa directed him to go to his father Kashyap Jee and ask for the food from him. So he went to Kashyap Jee and asked him some food to eat. Kashyap Jee directed him to an island where an elephant and a tortoise lived under the curse of each other. Garud Jee ate both of them.
[MBH, G-0-Prolog/7]

(9) Elephants in Mahaabhaarat
(1) Kuru's capital Hastinaapur also meant "The City of Elephants".

(2) There was one very famous elephant in MBH war too. He was with Bhagadatt. Bhagadatt's elephant's name was Supratikaa. He was a special elephant. Neither Bhagadatt, nor his elephant could be hurt in battle. In fact he had an armor on his body. Only Arjun or Krishn could break it. He was killed by Arjun by Vaishnav Astra in Mahaabhaarat war on 12th day, when Arjun was taken away from the battlefield in pursuit of capturing Yudhishthir. Bhagadatt got this armor from Narakaasur, the son of Prithvi. He used it to kill Arjun but Krishn took it on His chest, saved Arjun, and made Bhagadatt and his elephant ordinary.

(3) Another mention of an elephant comes in on the 15th day of the MBH war, when Drone became difficult to be killed. And if he was not killed he would have killed Paandav's lots of army. Krishn suggested that if somebody spreads the rumor of the death of Ashwatthaamaa, Drone's son, he would not put down his weapons and would not fight. All Paandav said - "But Ashwatthaamaa is immortal, how we can spread the rumor of his death and why should he believe on this news?" Krishn suggested - "If Yudhishthir will say this, he will believe it." But both Yudhishthir and Arjun did not approve this advice. Yudhishthir was made agreed with great difficulty. Then Bheem killed his own elephant of Indravarmaa of Maalavaa Region and shouted - "I have killed Ashwatthaamaa, I have killed Ashwatthaamaa." Indeed Drone did not believe this news until he had confirmed it from Yudhishthir.

General Mention of Elephants in Indian Scripture
According to Bhavishya Puraan, p 596 - Eight elephants are said to be born in Dev Yoni - (1) Kumud, (2) Airaavat, (3) Padm, (4) Pushpdant, (5) Vaaman, (6) Suprateek, (7) Anjan, and (8) Saarvbhaum.

[Valmiki Ramayan, 1/6]
Vaalmeeki Jee writes in his Raamaayan about the elephants in Ayodhyaa --
It is said that eight elephants from eight corners called Asht Diggaj support this Universe. And these eight elephants have their presiding deities. From those eight elephants, four are prominent - (1) Airaavat, the Elephant of Indra, (2) Anjan , the Elephant of Varun, the Rain-god, (3) Vaaman, the Elephant of Yam Raaj, the Lord of Death, and (4) Pundareek. Thus, the elephants of Ayodhya have been termed as of Divine breed.
       x        x      x       x       x
That city is always full with vigorous and mountain like elephants bred mainly from three classes viz., Bhadra, Mandra and Mrig. And inter-bred among these three main classes are Bhadra-Mandra, Mandra-Mrig, Bhadra-Mrig and the like. The Bhadra is the elephant class for King's ride, called Bhadra Gaj. It is a state elephant with high honors and for occasional or ceremonial use. Mandra and Mrig are classes of breed tamed and used in wars or for the ride of other nobility. These are the essential mammals used for other lifting and carrying works.

[V-Raamaayan, 2/14]
Raam gives one special elephant, given by His Maamaa, to Suyagya, Vashishth Jee's son, along with 1,000 elephants.

[Bhaagvat Puraan, 10/p14]
Kans had a very powerful elephant named Kuvalayaaped whom he prepared to kill Krishn when he invited Krishn to Mathuraa by Akroor Jee for his Dhanush Yagya. He made him drink lots of liquor and got mad to be able to kill Krishn.

Elephants and Horses - Measure of Power
In olden times the strength of a man was measured by elephant's power, for example Bheem had 10,000 elephants strength; but now it is measured in horse power

Both animals were used in war also.

General Information
In Mauryan times, only kings were allowed to own elephants. It was proof of their wealth and power.

In temples, one often finds images of lions subduing elephants. The lions are the symbols of the king, and the elephant represents the earth that the king rules over. She is rich, fertile and submissive.

In erotic literature, elephants are symbols of unrestrained raw sexual power. According to the Kaam Sootra, an elephant-woman or Hastinee is the lustiest of women, crude and vulgar in her carriage.

Buddha and Elephant
Buddha's mother dreamt of an elephant entering her womb, and the next day she declared that she was pregnant. The child grew up to become the Buddha. In his previous lifetime, so say the Jaatak, the Buddha was Vessantara, Prince of Shivi, who had in his stables a magical elephant that drew rain clouds wherever it went. And so, when there was a drought in Kaling, the King requested that Vessantara's elephant be sent there and draw in the rain.

Elephant In Japan
In Japan, the elephant-headed deity, Kangiten, is worshipped as a central object of devotion. Kangiten symbolizes conjugal affection, and is thus prayed to by couples hoping for children. Statues of this deity are relatively rare in Japan. Most are kept hidden from public view and are used in secretive rituals. Kangiten statues in Japan clearly reflect the deity's Hindu origins, for in India the deity is known as the elephant-headed Ganesh. In Japan, Kangiten is typically depicted with an elephant's head and human body, or as a pair of two-armed, elephant-headed deities in embrace.