Experimental studies indicate that 3D crystalline metal nanoclusters (NCs) intercalated under the surface of graphite have flat-topped equilibrated shapes. We characterize the shapes of these facetted NCs sandwiched between a blanketing graphene layer and the underlying graphite substrate. Specifically, we focus on the cases of fcc Cu and hcp Fe NCs. The analysis involves numerical minimization of the system energy for a specified NC volume and NC height, the latter corresponding to the separation between parallel top and bottom facets. Our numerical analysis quantifies how the distance of the side facet planes from center of the nanocluster varies linearly with a natural characteristic linear dimension of the nanocluster. Calculated shapes of fcc Cu and hcp Fe NCs are consistent with the hexagonal footprints observed in scanning tunneling microscopy studies.