We measured elastic moduli and hardness of polycrystalline SiO2 coesite. Translucent polycrystalline bulk coesite with a grain size of about 10 micrometers was fabricated at 8 GPa and 1600 degrees C using a Kawai-type multianvil apparatus. The obtained bulk and shear moduli are 94(1) and 60.2(3) GPa, respectively. The resulting Vickers and Knoop hardness values are 10.9(7) and 9.6(4) GPa, respectively, at an indentation load of 4.9 N. Coesite is as hard as other fourfold coordinated silica materials such as quartz and densified silica glasses. The hardness values of coesite and the fourfold coordinated silica materials are about one-third of those of sixfold coordinated silica materials, stishovite, and seifertite, which are the hardest known oxides.