The contact damage caused by the supporting pillar on the glass surface in vacuum glazing units is investigated. XFEM numerical modeling is employed to simulate the cone crack initiation and propagation. The critical indentation loads in localized uniform pressure and that for a cylindrical indenter are calculated and compared. The stress distributions due to the indenters of different geometries are investigated. In light of the numerical results, an improved design of supporting pillar is recommended, which is able to mitigate the severe concentration at the contact rim.