This island is just southwest of Island Purkey, separated from it by the narrow channel Selasund. The structure of the island is anorthosite, the light coloured type of rock on the moon (the other type is norite). The farm stands on the Windy Mound on the southeastern part of the island. The town Stykkisholmur is only about 7 km to its southwest. On a plain near the Skalli (Bald) Mound is an ancient, round ruin attached to a probable sheep shed ruin.
The day after the slaying of the country’s mightiest chieftain in 1241, Island Hrappsey is first mentioned in the Sagas. According to the Sturlunga Saga, Tumi Sighvatsson, the cousin of Snorri left farm Saudafell by the way of Hvammsfiord Bay for the Island Hrappsey. The island was good for farming in summer; sufficient fields for haymaking and winter grazings were good. Bird breeding colonies were large and bird hunting and eider down collecting good. According to Farm Registries from 1705 and 1731, the tenants paid their rent with eider down. In 1703, ten people lived on the island and eleven in 1731. Fourteen people were registered there in 1801 at two farms and in 1845 eighteen in one home. At that time Thorvaldur Sivertsen, a royal caretaker of the crown farms in the Skogarstrond District, lived there. His descendants lived on the island until the beginning of the 20th century. In 1926 thirteen people lived on the island and it was occupied until about 1958. Since then it has been exploited for winter grazings, hunting, egg and eider down collecting.
In 1773, Mr. Olafur Olafsson and his supporters installed the first independent printing works there. Many important books were printed there and the first periodical, News of the Month, was printed there in Danish for the Danish supporters of the venture. According to a legend, the house for the printing works was bought at a low price after its former owner had hanged himself in it. Many people claimed to feel and see his ghost in the house after it was moved to farm Stafafell from its original location and thereafter to Island Hrappsey. The island is a private property and unauthorized visits are not permitted.