In Homer's Iliad he is described as of great stature, colossal frame and strongest of all the Achaeans. Known as the "bulwark of the Achaeans", he was trained by the centaur Chiron (who had trained Ajax' father Telamon and Achilles' father Peleus and would later die of an accidental wound inflicted by Heracles, whom he was at the time training), at the same time as Achilles. He was described as fearless, strong and powerful but also with a very high level of combat intelligence. Ajax commands his army wielding a huge shield made of seven cow-hides with a layer of bronze. Most notably, Ajax is not wounded in any of the battles described in the Iliad, and he is the only principal character on either side who does not receive substantial assistance from any of the gods who take part in the battles, although, in book 13, Poseidon strikes Ajax with his staff, renewing his strength. Unlike Diomedes and Achilles, Ajax appears as a mainly defensive warrior, instrumental in the defence of the Greek camp and ships and that of Patroclus' body. When the Trojans are on the offensive, he is often seen covering the retreat of the Achaeans. Significantly, while one of the deadliest heroes in the whole poem, Ajax has no aristeia depicting him on the offensive.

Ajax, or Aîas (Of the earth) son of Telamon, king of Salamis, a legendary hero of ancient Greece. To distinguish him from Ajax, son of Oileus, he was called "Ajax the Great" or "Telamonian Ajax". In Homer's Iliad he is described as of great stature and colossal frame, second only to Achilles in strength and bravery, and the 'bulwark of the Achaeans'. He is not wounded in any of the battles described in the Iliad, and he is the only principal character on either side who does not receive personal assistance from any of the gods who take part in the battles.

During the Trojan War, Ajax fought Hector while Achilles sulked over an argument with Agamemnon. Ajax wounded but did not kill him. He did kill Phorcys. During the fight over the body of Patroclus, his prayer to the gods to clear the fog which has descended over the battle is promptly granted by Zeus. In Homer's Odyssey, with the aid of Athena, Ajax rescued the body of Achilles from the hands of the Trojans. In the competition between him and Odysseus for the armour of Achilles, Agamemnon, at the instigation of Athena, awarded the prize to Odysseus. This so enraged Ajax that it caused his death (Odyssey, xi. 541). According to a later and more detailed story, his disappointment drove him mad; he rushed out of his tent and fell upon the flocks of sheep in the camp under the impression that they were the Trojan enemy; on coming to his senses, in shame he killed himself with the sword which he had received as a present from Hector. This is the account of his death given in the Ajax of Sophocles; in Pindar's "Nemea", 7; and in Ovid, Metamorphoses, xiii. 1). From his blood sprang a red flower, as at the death of Hyacinthus, which bore on its leaves the initial letters of his name Ai, also expressive of lament (Pausanias i. 35. 4). His ashes were deposited in a golden urn on the Rhoetean promontory at the entrance of the Hellespont.

Like Achilles; he is represented as living after his death in the island of Leuke at the mouth of the Danube (Pausanias iii. 19. 11). Ajax, who in the post-Homeric legend is described as the grandson of Aeacus and the great-grandson of Zeus, was the tutelary hero of the island of Salamis, where he had a temple and an image, and where a festival called Aianteia was celebrated in his honour (Pausanias i. 35). At this festival a couch was set up, on which the panoply of the hero was placed, a practice which recalls the Roman lectisternium. The identification of Ajax with the family of Aeacus was chiefly a matter which concerned the Athenians, after Salamis had come into their possession, on which occasion Solon is said to have inserted a line in the Iliad (book ii. 557 or 558), for the purpose of supporting the Athenian claim to the island. Ajax then became an Attic hero; he was worshipped at Athens, where he had a statue in the market-place, and the tribe Aiantis was called after his name.