First-principles calculations of the crystal structure and elastic properties of a range of oxyorthosilicates R 2 SiO 5 (R denotes rare-earth ion) are performed in the framework of density functional theory (DFT) with hybrid functionals. The elastic moduli, sound velocities, Debye temperature, and minimum thermal conductivity coefficient are calculated for Lu 2 SiO 5 in good agreement with the experiment, and a prediction of these parameters for a range of R 2 SiO 5 is made. It is shown that La 2 SiO 5 and Pr 2 SiO 5 have the minimum thermal conductivity from a range of oxyorthosilicates.