Olaf Gudrødsson, or as he was named after his death Olaf Geirstad-Alf, was a legendary Norwegian king of the House of Yngling from the Ynglinga saga. He was the son of Gudrød the Hunter and according to the late Heimskringla, the half-brother of Halfdan the Black. Gudrød and Olaf conquered a large part of Raumarike.
- Long while this branch of Odin's stem
- Was the stout prop of Norway's realm;
- Long while King Olaf with just pride
- Ruled over Westfold far and wide.
- At length by cruel gout oppressed,
- The good King Olaf sank to rest:
- His body now lies under ground,
- Buried at Geirstad, in the mound.
After his death, Olaf was worshipped as an elf, and was called the Geirstad-alf (the "elf of Geirstad").
A hypothesis identifies Geirstad with Gjerstad near Gokstad, and his burial with the Gokstad Ship.