The Young's and shear moduli of polycrystalline monoclinic hafnium oxide were determined by the sonic resonance method at room temperature as a function of volume fraction porosity. The Spriggs equation empirically described the data and the zero porosity moduli as 283.6 GN/m² and 109.2 GN/m² for Young's and shear moduli, respectively. The Debye temperature calculated from the elastic constants was 484°K. Several specimens had anomalously low moduli values, attributed to microcracking. Grain size and internal friction measurements showed that the microcracking occurred in specimens with grain sizes > 2 to 3 μm and was characterized by high internal friction.