A method for synthesizing YSAG:Yb optical ceramics has been developed. Additionally, the phase composition and unit cell parameters for YSAG, YbSAG, and their solid solutions have been determined. The limits of scandium solubility in the dodecahedral and octahedral sites of garnet crystal lattice have been estimated after annealing at 1600 degrees C. The scandium solubility limit in the dodecahedral sites of YSAG:Yb was found to be 66 +/- 2 at.%. The limit of scandium solubility in octahedral sites depended upon the type of garnet-forming cations. The solubility limit for Sc3+ decreased from 97.5 +/- 0.5 to 68.5 +/- 1 at.% with simultaneous increase of ytterbium content in the YSAG-YbSAG system. Therefore, the region of solid solutions existing with a garnet structure in the Al2O3-Sc2O3-Yb2O3-Y2O3 system was determined. Samples having scandium in both dodecahedral and octahedral sites, which had a Sc3+ content of 30 at.%, were synthesized as a precursor for optical ceramic production.