Xerogels and powders of a solid solution based on zirconium dioxide are synthesized by the method of coprecipitation of hydroxides from aqueous solutions of salts of zirconium nitrate ZrO(NO3)2⋅2H2O, aluminum Al(NO3)3⋅9H2O, and cerium Ce(NO3)3⋅9H2O with an aqueous 1 M solution of ammonia NH4OH. A dense ceramic with low porosity and water absorption is obtained. The effect of the ultrasonic treatment of the precipitate and mechanical treatment of the xerogel on the physicochemical properties of the obtained materials is evaluated.