Hesiod provided a different folk etymology in a story in his "The Great Eoiae", where Ajax receives his name when Heracles prays to Zeus that a son might be born to Telemon and Eriboea: Zeus sends an eagle (aetos αετός) as a sign, and Heracles then bids the parents call their son Ajax after the eagle.

On an Etruscan tomb dedicated to Racvi Satlnei in Bologna (5th century BC), there is an inscription that says aivastelmunsl, which means "[family] of Telamonian Ajax".

In Book 9, Agamemnon and the other Mycenaean chiefs send Ajax, Odysseus and Phoenix to the tent of Achilles in an attempt to reconcile with the great warrior and induce him to return to the fight.

Ajax's prayer to Zeus to remove the fog that has descended on the battle to allow them to fight or die in the light of day has become proverbial.

When Achilles dies, killed by Paris (with help from Apollo), Ajax and Odysseus are the heroes who fight against the Trojans to get the body and bury it with his companion, Patroclus.

[12] Ajax, with his great shield and spear, manages to recover the body and carry it to the ships, while Odysseus fights off the Trojans.

[13] After the burial, each claims Achilles' magical armor, which had been forged on Mount Olympus by the smith-god Hephaestus, for himself as recognition for his heroic efforts.

Ajax argues that because of his strength and the fighting he has done for the Greeks, including saving the ships from Hector, and driving him off with a massive rock, he deserves this magical protection.

Athena intervenes and clouds his mind and vision, and he goes to a flock of sheep and slaughters them, imagining they are the Achaean leaders, including Odysseus and Agamemnon.

When he comes to his senses, covered in blood, he realizes that what he has done has diminished his honor, and decides that he prefers to kill himself rather than live in shame.

[18] 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.

[21] 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.

[20] Pausanias also relates that a gigantic skeleton, its kneecap 5 inches (13 cm) in diameter, appeared on the beach near Sigeion, on the Trojan coast; these bones were identified as those of Ajax.

In 2001, Yannis Lolos began excavating a Mycenaean palace near the village of Kanakia on the island of Salamis which he theorized to be the home of the mythological Aiacid dynasty.

The palace appears to have been abandoned at the height of the Mycenaean civilization, roughly the same time the Trojan War may have occurred.