Abstract: Preparation of lutetium and yttrium aluminate single crystals doped with rare earth oxides and transition elements consists in the preparation of oxide mixture sinter which is melted throughout and homogenized for a period of at least one hour. The crystal growth rate and broadening of the crystal cone are maintained uniform at an angle of at least 60° from the crystal axis up to a diameter of at least 80% of the crucible diameter which is at least 100 mm. The completion of the process occurs by separating the crystal from the melt while the crystal continues to be positioned inside the crucible in the zone wherein it was grown, and wherein final tempering of the crystal also takes place.