In 2003 and 2004, he published a three-volume work which doubled as his PhD dissertation, cataloguing the finds from Barshalder [sv; de], the largest prehistoric cemetery on the Swedish island of Gotland.

[R 1] Excavating years later at one of these sites, Aska [sv], Rundkvist uncovered the foundations of a large mead hall, and 30 ornate gold figures that might have represented gods or royals.

In other works, Rundkvist has excavated a Viking boat grave, and analysed both the placement of deposited artefacts in the landscape and the lifestyles of the Scandinavian élite during the Middle Ages.

[11] Rundkvist is also a member of the Internationales Sachsensymposion,[R 3] an international society formed to study Germanic Saxons and the relationships between these populations and those in countries bordering the North and Baltic Seas.

[R 16] The topic was suggested by Jan Peder Lamm, who discovered important unpublished finds from the cemetery while organising the Swedish History Museum's stores, and declared that it would take "a foolish and stubborn person" to gather and publish the artefacts and notes from nearly two centuries of excavation.

[R 17][23] The works were reviewed in Antiquity as "a good thorough contextual study", and noted for offering "an elegant explanation" for clustered Viking Age graves, which Rundkvist argued represented grandparents and their grandchildren rather than a nuclear family.

[31] Rundkvist ultimately identified nine areas as regional power centres, where mead halls may have stood, during parts of the Late Roman Period through Viking Age.

[R 26] Given the region's comparatively humble finds, and the diffuse nature of Rundkvist's landscape descriptions—such as to look for where water "does something interesting"—several reviewers wrote that it would be difficult to translate his heuristic principles to the field, as intended;[32][33] one termed it a "curate's egg".

It built on Rundkvist's two decades of fieldwork in the area, including excavations of four of its twenty-five castles,[39] and marked his entry into "the historically documented part of our province's past".

[40] The work analysed the lifestyles of those who lived in castles in Östergötland around 1200–1530 AD; modifying a common saying about World War I, Rundkvist termed such existence "decades of boredom punctuated by weeks of terror".

[40] Another wrote that the book was full of "small but enlightening chapters" and that it "conducts researchers and other readers to an archaeological trip through the Swedish castles alongside the margins of the Baltic Sea".

[44][45] The son of a priest and illegitimate grandson of the Queen's brother, Kiöping had written about his travels from 1648 to 1656 along the coasts of Africa, Arabia and southern Asia, and an autobiographical essay first published posthumously in 1773.

[R 31] Known primarily for a rich 10th-century burial excavated in 1920 by Ture J:son Arne [sv],[46] Aska also has a large and oddly shaped mound, which Rundkvist described as "oval and flat-topped, like a raised tennis court".

[R 33] In April 2013, Rundkvist and his colleague Andreas Viberg surveyed the mound with ground-penetrating radar, discovering evidence of a mead hall measuring 47.5 metres (156 feet) long and up to 14 m (46 ft) wide.

[R 36] The dig uncovered part of the foundations of the mead hall from around 700 AD,[50] including post holes,[51] and artefacts such as two whale-bone gaming pieces, an iron pendant, flint flakes used to make fires, and a decorative Vendel Period shield mount.

[52][50][53][54] Speaking to Sveriges Television, Rundkvist described it as only the third find of such figures in Östergötland, and said they may have represented the gods or royals;[55][56] they may originally have been attached to support posts or high seats.

[R 40] Their survey reported finds to the west, suggesting the presence of both a settlement site and burials, including five brooches from the Early Vendel Period and fragmented copper-alloy jewellery from the Middle Viking Age.