Geirsholmur is a round shaped, rocky islet near the Thyrill Headland on the Whale Bay.
Whale Bay is mentioned in the Sagas of the Sturlungar and Hordur and the Islanders. Hordur was the leader of a band of robbers who occupied the islet for a while. They were tricked ashore and killed, but before Hordur was killed he managed to slay 13 of his attackers.His wife, Helga the earl’s daughter, and their two sons, 4 and 8, remained on the islet because she suspected foul play. She swam ashore with the younger boy on her back and the older one coped on his own. They managed to cross the mountains to the Skorradalur Valley, where they were kept safe. Later, during the troubled Sturlungar Period, a group of Sturla Sighvatsson’s men stayed on the islet for a while and did much the same as Hordur and his companions.
The churches on the island were annexed to the parish church of Thonglabakki in the past and their patron saint during catholic times was The Holy Virgin. In 1884, the church was abolished and in 1960, it was reconsecrated. Flatey has not been inhabited for a few decades but many people spend their summers there for relaxation, the reaping of the natural resources, and the fisheries.