The burial attributed to Saint Éinne, the early Christian founder associated with the monastic complex known as Teaghlach Éinne, or the Household of Éinne, has no visible surface trace. The ground simply offers nothing.

The structure was most likely a leacht, a term for a small commemorative stone monument, typically a low cairn or slab arrangement associated with a saint or a place of early Christian devotion. In 1684, the writer Roderic O'Flaherty noted that the covering stone was still visible. By the mid-nineteenth century, that stone, along with the graves of 120 saints said to be located to the north-east of the church, had all been consumed by the drifting sand. The site was never marked on the Ordnance Survey six-inch maps, which suggests that even at the time those surveys were being conducted, there was little or nothing left to indicate. The dunes in this part of Inishmore are not static; they move, accumulate, and bury, and they have been doing so for a very long time. During excavations at the church in 1984, a setting of slabs was uncovered on the north side of the building, a feature tentatively identified as a grave marker, possibly one of the burials on the edge of the ancient graveyard. Whether it relates to Éinne's grave directly remains uncertain.

The graveyard itself is still an active and well-defined site, and the church ruins of Cill Éinne remain visible. What the landscape communicates, though, is absence rather than presence: a famous grave that has been technically located, briefly glimpsed in the historical record, and then quietly lost again beneath the sand.