Y-Si-O-N quaternary oxynitrides ( Y5Si3O12N, Y4Si2O7N2, YSiO2N, Y2Si3O3N4, and Y3Si5ON9) are recognized as important secondary grain-boundary phases in silicon nitride and believed to have important impacts on the high-temperature mechanical properties and thermal conductivity of Si3N4 ceramic. In this work, equilibrium crystal structures, theoretical mechanical properties ( second-order elastic constants, polycrystalline bulk modulus, shear modulus, Young's modulus, and Vickers hardness) of the five quaternary phases are calculated using first-principle total energy calculations. Meanwhile, temperature dependence of thermal conductivities of all five compounds is obtained based on Debye-Clarke model and Slack equation. On the basis of theoretical prediction, we establish the relationship between the componential ( cation/anion or cation/cation ratios) and structural characteristics ( bonding configurations) and mechanical/thermal properties. Our results are expected to provide helpful guidelines to improve the performances of Y-Si-O-N ceramics, and further guide the optimization of mechanical and thermal properties of Si3N4 by properly tailoring the secondary grain-boundary phases.