Euryale was born in the depths of the sea, the daughter of Phorcys, an ancient sea god who was the son of Pontus, the primordial sea itself, and Ceto, a sea goddess whose name means "Whale" or "Sea Monster." Her siblings were numerous and terrible: the Graeae, three sisters who shared a single eye and a single tooth between them; Echidna, the half-woman half-serpent mother of monsters; the serpent Ladon, who coiled around the tree of golden apples in the garden of the Hesperides; and the three Gorgons themselves: Stheno, Euryale, and Medusa. The poet Hesiod, writing in the eighth or seventh century BCE, describes them in his Theogony as dwelling in the western ocean beyond the pillars of the world, near the garden of the Hesperides, the nymphs who tended the tree of golden apples sacred to the goddess Hera. The Gorgons were unlike anything else in creation. They had great wings of gold, hands of bronze, and hair that was alive with venomous serpents. Their faces were so terrible that any mortal who looked directly upon them was turned instantly to stone, and their gaze was said to petrify even the gods themselves.

Of the three sisters, Stheno was the eldest and the most violent, having killed more men than her two sisters combined. Euryale was the middle sister, her name meaning "Wide-Wandering" or "Far-Springer," and she shared her elder sister's immortality. Medusa, the youngest, was different. She alone among the three was mortal, and she alone was beautiful, or at least had been beautiful before Athena, the goddess of wisdom and war, cursed her for desecrating her temple by lying with Poseidon within its walls. In some accounts Medusa was born monstrous, but the more famous tradition, recorded by Ovid in his Metamorphoses, makes her transformation a punishment. This distinction between mortal and immortal would prove fatal for Medusa and would leave Euryale and Stheno to mourn her forever.

The hero who would destroy their sister was Perseus, the son of Zeus and Danae, a princess of Argos whose father had locked her in a bronze tower to prevent her from bearing a child. Perseus was sent on his quest by Polydectes, the king of Seriphos, who wanted to marry Danae and had sent the young man to fetch the head of Medusa as a pretended wedding gift, expecting him to die in the attempt. But Perseus was aided by the gods. Athena gave him a polished bronze shield so that he could see Medusa's reflection without looking directly at her face. Hermes, the messenger god, gave him a curved sword of adamant, the hardest metal known to the gods. He received winged sandals from the nymphs, a cap of darkness from Hades that made him invisible, and a special pouch to carry the severed head. Flying west across the sea, he reached the cave of the Gorgons and found them asleep, their serpent hair writhing even in slumber.

Perseus approached Medusa, using Athena's shield as a mirror to guide his blade. He struck off her head in a single blow, and from her severed neck sprang two children: Pegasus, the winged horse, and Chrysaor, the warrior with the golden sword, both fathered by Poseidon. The noise of the murder woke Euryale and Stheno. The poet Ovid describes the scene in the Metamorphoses: the two immortal sisters rose from their beds, saw their sister's body and the blood that flowed from the wound, and let out a shriek so terrible that the very heavens trembled. They spread their golden wings and flew in pursuit of Perseus, who had already seized the head and was flying eastward with the winged sandals. But Perseus was invisible in the cap of Hades, and his winged sandals carried him faster than the Gorgons could fly. They chased him across the sky, their shrieks echoing through the clouds, but they could not catch him. He escaped to Seriphos, and from there the head of Medusa would travel across the Greek world, turning the sea monster Cetus to stone, turning Atlas to stone, and finally being given to Athena, who fixed it upon her shield, the aegis.

Euryale and Stheno were left with their grief and their immortality. They could not die, and they could not be killed, and they could not bring their sister back. In some traditions, recorded by the mythographer Apollodorus, the two surviving Gorgons appear again in the story of Perseus's later adventures, but their role is always as the mourners, the ones who were left behind. In a lesser-known tradition, Euryale was said to have been the mother of Orion, the giant hunter, by Poseidon. This tradition, recorded in some late sources, gives Euryale a child who would rival the gods in size and strength, a fitting legacy for one of the most terrible monsters in the Greek world. But the primary tradition leaves her as the immortal sister who woke to find her sibling murdered and could do nothing but scream at the empty sky.

The Gorgons were not merely monsters in the Greek imagination. They were protective figures as well, their severed heads carved on shields, temples, and tombs to ward off evil. The image of the Gorgoneion, the Gorgon head, became one of the most common symbols in Greek art, appearing on the shields of Athena, on the coins of cities, and at the entrances of sacred places. Euryale's face, though less famous than Medusa's, was part of this protective power. The poet Hesiod says that the Gorgons lived near the entrance to the underworld, and their presence marked the boundary between the world of the living and the world of the dead. In this sense, Euryale was not merely a monster to be slain but a guardian of the threshold, a creature who stood at the edge of the world and kept the living from straying too far into the dark.