As promising candidates for ultrahigh temperature applications, high-temperature properties, which are quite rare and fragmentary, have great significance to ZrB2 and HfB2. In this work, thermodynamic and mechanical properties of ZrB2 and HfB2 from 0 K to 2000 K were investigated by a combination of first principles calculations and quasi-harmonic approximations. The ground-state properties, including lattice parameters, elastic constants, phonon dispersion, and mode-Gruneisen parameters are calculated. The theoretical thermal expansion, elastic and thermodynamic properties at elevated temperatures show good agreement with experiments. By discussing Gruneisen parameters anisotropy, the mechanism for the thermal expansion anisotropy of ZrB2 and HfB2 is uncovered. The influence of direction-dependent sound velocities on the anisotropy of thermal conductivity is also discussed.