What is the name of the oldest surviving epic poem?

The oldest surviving epic poem is the Epic of Gilgamesh.

This Mesopotamian work began as separate Sumerian poems about Gilgamesh, the legendary king of Uruk. Those stories were later combined into an Akkadian epic, whose earliest surviving unified version dates to around the 18th century BCE. The poem was written in cuneiform on clay tablets in what is now Iraq.

Its best-known surviving form is the Standard Babylonian version, associated with the scholar-priest Sîn-lēqi-unninni and generally dated between the 13th and 10th centuries BCE. The narrative follows Gilgamesh’s friendship with Enkidu, their adventures, Enkidu’s death, and Gilgamesh’s search for meaning and immortality.

A common mix-up is naming Homer’s Iliad or Odyssey. Those are enormously influential epics, but they were composed much later, probably in the 8th century BCE. “Oldest surviving” refers to the age of the preserved literary tradition, not necessarily the oldest story ever told.