Mechanical properties of a defect-free bulk GaN single crystal has been studied by nanoindentation in the C (0001) surface. Our experiments provide consistent evaluations of Young's modulus (E = 320 GPa) measured with both Berkovich and spherical indenters. Additionally, Berkovich hardness (H = 17 GPa) and true hardness (Ht = 25 GPa) were determined. Pop-in events are confirmed to indicate the elastic-plastic transition of the material, and give also consistent yield (maximum) shear stress, τmax = 19 GPa, for both the indenters. To achieve these precise analyses, the effective curvature of the indenter was determined by the Hertz analysis of the contact between the indenter and a diamond crystal, in addition to the Oliver-Pharr method with a standard fused quartz.