In this contribution, the structural, mechanical, and thermal properties of MSiO 4 have been investigated theoretically and the anisotropy of elastic properties has been discussed in detail. The heterogeneous bonding nature was revealed from density functional theory computations and chemical bond theory (CBT). The Young's modulus and shear modulus of MSiO 4 were anisotropic and the anisotropy on different planes was quite different. The thermal expansion coefficients of MSiO 4 estimated from CBT were 5.1 Â 10 À6 and 4.4 Â 10 À6 K À1 for ZrSiO 4 and HfSiO 4 , respectively. These results were quite consistent with the experiments. The temperature dependent thermal conductivities of MSiO 4 were estimated from Slack's model, the minimum thermal conductivity was predicted to be 1.54 and 1.24 W m À1 K À1 for ZrSiO 4 and HfSiO 4 , respectively. Our theoretical results show that MSiO 4 are excellent thermal barrier materials with good tolerance to withstand the mechanical damage.