Atlantis, which means "daughter of Atlas" in Greek, is first mentioned in Plato's dialogues Timaeus and Critias, though Critias was never finished. Benjamin Jowett argues that Plato originally planned a third dialogue titled Hermocrates. John V. Luce goes further arguing that Plato, after describing the origin of the world and mankind in Timaeus and the allegorical perfect society of ancient Athens and its successful defense against an antagonistic Atlantis in Critias, would have made the strategy of the Greek civilization during their conflict with the Persians a subject of discussion in the Hermocrates.

In his account, Atlantis was a naval power that conquered many parts of Western Europe and Africa 9,000 years (approximately 9600 BC) before the time of Solon, the great, great grandfather of Critias, who was told the story by Egyptian priests of Sais, who translated the history of ancient Athens and Atlantis, recorded on papyri in Egyptian hieroglyphs, into Greek.

For it is related in our records how once upon a time your State stayed the course of a mighty host, which, starting from a distant point in the Atlantic ocean, was insolently advancing to attack the whole of Europe, and Asia to boot. For the ocean there was at that time navigable; for in front of the mouth which you Greeks call, as you say, 'the pillars of Heracles,' there lay an island which was larger than Libya and Asia together; and it was possible for the travelers of that time to cross from it to the other islands, and from the islands to the whole of the continent over against them which encompasses that veritable ocean. For all that we have here, lying within the mouth of which we speak, is evidently a haven having a narrow entrance; but that yonder is a real ocean, and the land surrounding it may most rightly be called, in the fullest and truest sense, a continent. Now in this island of Atlantis there existed a confederation of kings, of great and marvelous power, which held sway over all the island, and over many other islands also and parts of the continent.

According to Plutarch, Solon met with "Psenophis of Heliopolis, and Sonchis the Saite, the most learned of all the priests"; Plutarch refers here to events that would have happened five centuries before he wrote of them.

In Critias, the Hellenic gods divided the land so that each god might own a lot; Poseidon was bequeathed the island of Atlantis. The island was larger than Ancient Libya and Asia Minor combined. The Egyptians, Plato asserted, described Atlantis as an island comprising mostly mountains in the northern portions and along the shore, and encompassing a great plain of an oblong shape in the south "extending in one direction three thousand stadia [about 555 km; 345 mi], but across the center inland it was two thousand stadia [about 370 km; 230 mi]." Fifty stadia (9 km; 6 mi) from the coast was a mountain that was low on all sides... broke it off all round about... the central island itself was five stades in diameter [about 0.92 km; 0.57 mi].

In Plato's myth Poseidon fell in love with Cleito, the daughter of Evenor and Leucippe, who bore him five pairs of male twins. The eldest of these, Atlas, was made rightful king of the entire island and the ocean (called the Atlantic Ocean in his honor), and was given the mountain of his birth and the surrounding area as his fiefdom. Atlas's twin Gadeirus, or Eumelus in Greek, was given the extremity of the island towards the Pillars of Heracles. The other four pairs of twins — Ampheres and Evaemon, Mneseus and Autochthon, Elasippus and Mestor, and Azaes and Diaprepes — were also given "rule over many men, and a large territory." Poseidon carved the mountain where his love dwelt into a palace and enclosed it with three circular moats of increasing width, varying from one to three stadia and separated by rings of land proportional in size. The Atlanteans then built bridges northward from the mountain, making a route to the rest of the island. They dug a great canal to the sea, and alongside the bridges carved tunnels into the rings of rock so that ships could pass into the city around the mountain; they carved docks from the rock walls of the moats. Every passage to the city was guarded by gates and towers, and a wall surrounded each of the city's rings. The walls were constructed of red, white and black rock quarried from the moats, and were covered with brass, tin and the precious metal orichalcum, respectively.

According to Critias, 9,000 years before his lifetime a war took place between those outside the Pillars of Hercules at the Strait of Gibraltar and those who dwelt within them. The Atlanteans had conquered the parts of Libya within the Pillars of Heracles as far as Egypt and the European continent as far as Tyrrhenia, and subjected its people to slavery. The Athenians led an alliance of resistors against the Atlantean empire, and as the alliance disintegrated, prevailed alone against the empire, liberating the occupied lands.

After the failed attempt to invade Athens, Atlantis sank into the ocean "in a single day and night of misfortune" and became an impassable mud shoal, inhibiting travel to any part of the ocean.