Graphite at the nanoscale is modeled as a material system consisting of a stack of parallel plates buffered by an elastic material. While the plates represent individual graphene sheets, the buffer material models the Van der Waals interaction between the graphene sheets. As such, the loading on graphite at the nanoscale is characterized by the membrane force, the bending moment, and the shear force in the graphene sheets. Cylindrical nanoindentation of graphite is analyzed by applying a special boundary element method that employs Green’s function for multilayers with platelike interfaces. Because Green’s function satisfies the traction-free surface, the interfacial displacement continuity and the interfacial traction discontinuity conditions, only the indentation surface area where the boundary condition is altered, are numerically discretized. Numerical results of cylindrical nanoindentation are presented. It is shown that the bending moment and the shear force in the graphene sheets are concentrated around the edge of contact, consistent with the singularities existing in the second and the third derivatives of the surface displacement in the reduced case of a semi-infinite homogeneous solid under cylindrical contact. Kinks of single, double, and triple joints are related to the bending moment, the shear force, and the concentrated force, respectively.