We performed the thermal stress analyses of lead molybdate (PbMoO4) bulk single crystals for the various growth directions, using a three-dimensional finite element computer code developed to deal with the thermal stress analyses of tetragonal single crystals during growth process. The computer code takes account of the crystal anisotropy in elastic constants and thermal expansion coefficients. In the computer code, the tensor transformation technique is used to obtain the components of the elastic constant matrix and thermal expansion coefficient vector corresponding to an arbitrary growth direction, so it enables to perform the thermal stress analysis of all arbitrary growth direction. Based on the thermal stress analyses of the lead molybdate bulk single crystals, we made a detailed discussion on the relation between the thermal stress and the crystal quality, especially focusing oil the generation of subgrains. (c) 2005 Elsevier B.V. All rights reserved.