A field emission display has spacers separating the emitting base and display face. The arrangement of the spacer is important for maintenance of required clearance, endurance of bending stresses, and efficient vacuum sealing. Topology optimization technique with material density was introduced to select the best position of the spacers from the available positions. The displacement and Von Mises stress distribution of the panels with optimal spacers were calculated by finite element method. Also the design guide for adding eliminating spacers was proposed.