A 2 × 2 × 1 supercell of ␣-Si 3 N 4 is used to model Y-doped ␣-SiAlON's (silicoalumino oxonitrides). Ab initio total energy calculations are performed at the DFT (GGA) level. A full relaxation of atomic positions is performed for stoichiometric ␣-Si 3 N 4 and for a series of substituted structures with concentrations of Y, Al and O increasing up to the composition Y 0.5 Si 9.5 Al 2.5 O 1.0 N 15.0 , similar to the observed solubility limits. The avoidance of neighboring AlX 4 (X = N,O) tetrahedra in highly doped structures indicates that the distribution of Al atoms in the framework of ␣-SiAlON's obeys the same Loewenstein rule as in aluminosilicate zeolite structures. An increase of the lattice parameters and cell volumes is observed with increasing degree of the doping. Changes are more pronounced for the insertion of Y than for Si-N/Al-O substitution. An introduction of a Y 3+ cation into the interstitial position in the cage, however, causes a local contraction of the structure. Via the contraction a more efficient Y-N bonding is formed, leading to the stabilization of the Y-doped structure. The pronounced increase of the cell volume and the lattice parameters with Y-doping is due to three framework Al/Si framework substitutions compensating the extraframework Y 3+ cation. The calculated bulk modulus (B 0 ) ranges from 223 GPa for pure ␣-Si 3 N 4 to 197 GPa for Y 0.5 Si 9.5 Al 2.5 O 1.0 N 15.0 . The slope of the decrease of B 0 with the degree of doping depends on the Y-content. For constant concentration of Y an increasing content of O causes a linear decrease of B 0 .