They were not discovered until 1975, when a bulldozer broke through the ground and, in the process, shattered one of the urns that had held them.

A cist is a small box-like burial chamber, typically constructed from flat stone slabs, used across Bronze Age Europe to contain the dead. The Glenacunna example was rectangular, roughly a metre long and just under a metre wide, aligned northeast to southwest, and divided internally into two compartments, each sealed above by a shared capstone. Inside each compartment, a cinerary urn, a ceramic vessel used to hold cremated remains, had been placed upside down on a floor slab. Both urns contained cremated human bones. The urn at the northeastern end held the remains of a person aged approximately fifteen or sixteen years, while the one at the western end contained those of an adult male. The northeastern urn, the one fractured by the bulldozer, also held a small miniature vessel, a type of object sometimes found accompanying Bronze Age burials, though its precise purpose remains a matter of interpretation. The cist has been dated to the Early Bronze Age, somewhere between 1700 and 1400 BC. A second grave was found about twelve metres to the west, though it had been badly disturbed by the same machinery that uncovered the first.