The Al2O3-Nd2O3-SiO2-Y2O3 pseudoquaternary system was thermodynamically modeled with a focus on the phase equilibria concerning the sintering of neodymium-doped yttrium aluminum garnet, Nd:YAG ((Y1-xNdx)(3)Al5O12). The Nd2O3-SiO2 and Nd2O3-Y2O3 systems were evaluated. Due to the lack of experimental thermochemical data, first-principles calculations were used to predict the enthalpy of formation of Nd2SiO5 and the enthalpy of mixing of Nd in YAG. Isothermal sections of the Al2O3-Nd2O3-SiO2, Al2O3-Nd2O3-Y2O3, and Nd2O3-SiO2-Y2O3 pseudoternary systems are presented.