The surface Young's modulus (E) and hardness (H) of fused silica samples have been studied by nanoindentation. Two factors strongly affect the results of E and H. One factor is the polishing quality of the fused silica surface. Poor polishing quality produces much smaller E and H than the literature values for bulk fused silica. The second factor is surface flatness. Even for a well-polished silica surface, an "arch bridge effect" may hinder the measurements of the true values of E and H. A correction procedure is proposed to eliminate this effect, and the corrected results show substantial improvements.