The burial ground at Graigaheesha sits on flat pasture with open views in every direction, and while the inscribed stones inside date from the eighteenth and nineteenth centuries, the enclosure that contains them belongs to a much earlier tradition entirely. The graveyard is circular, roughly 33 metres across, and the boundary around it is not simply a wall but a layered defensive arrangement: a limestone rubble wall, then a flat berm, then a waterlogged fosse (a ditch, typically used as a barrier or boundary feature), and finally a well-preserved wide, flat-topped outer bank. That combination of elements points to an origin long predating the headstones within.

Circular enclosures of this kind in Ireland are frequently associated with early medieval ecclesiastical sites, where the sanctity of the ground was marked and protected by concentric earthworks rather than simple walling. The enclosure here follows that pattern closely. The entrance is a causewayed gap on the east side, just one and a half metres wide, which is the typical orientation for early Christian sites, where the rising sun carried liturgical significance. At the western end of the graveyard, stone footings survive that may represent the south-west gable of a church, which would reinforce the ecclesiastical reading of the site. A ringfort, a type of circular farmstead enclosure common across early medieval Ireland, lies approximately 430 metres to the south-east, suggesting that this corner of Tipperary was an organised, inhabited landscape during that period. The outer bank, which disappears at the western sector, otherwise survives in notably good condition for a monument of this age sitting in working agricultural land.