Yttrium aluminum garnet (YAG, Y3Al5O12) and yttrium aluminum garnet doped with neodymium (Nd:YAG) single crystals were grown by the Czochralski technique. The critical diameter and the critical rate of rotation were calculated. Suitable polishing and etching solutions were determined. As a result of our experiments, the transparent YAG and pale pink Nd:YAG single crystals were produced. The obtained crystals were studied by X-ray diffraction, Raman and IR spectroscopy. The crystal structure was confirmed by XRD. The 15 Raman and 17 IR modes were observed. The Raman and IR spectroscopy results are in accordance with X-ray diffraction analysis. The obtained YAG and Nd:YAG single crystals were without core and of good optical quality. The absence of a core was confirmed by viewing polished crystal slices. Also, it is important to emphasize that the obtained Nd:YAG single crystal has a concentration of 0.8 wt.% Nd3(+) that is characteristic for laser materials. (C) 2014 The Authors. Published by Elsevier Ltd.