There are many versions of the flood myth in stories from ancient Mesopotamia, and there is indeed an account of it in several versions of the Epic of Gilgamesh, an epic poem about the king and hero Gilgamesh and his quest for immortality. During one of his adventures he meets Utnapishtim, who had built a ship in order to save his family, friends, and all creatures from the Great Deluge, and who had become immortal as a result.
As another user has indicated, the account of the flood in the Epic of Gilgamesh has significant parallels to the Flood of Noah in the Book of Genesis.