Small-scale solidification simulations were carried out in order to study the effect of the grain orientation and cooling rate on the stresses in mono- and bi-crystals. First, a 2D-axisymetric heat-transfer model of the global furnace is established to provide input to the sub-model. The sub-model takes into account only the crucible and silicon ingot. The flux histories are transferred from the global model. A finite element crystal plasticity model solves the mechanical deformation in the ingot. Ingots were grown in the small-scale Bridgman furnace with different pulling rates ranging from 0.2 to 50 mm/min. The results show the asymmetric effect of the crystal orientation and the stress build-up at the grain boundary due to different orientations. The change in pulling rate affects strongly the solidification front shape and the residual stresses. The 3D mechanical model illustrates also the limitations of the 2D-axisymmetric approach when silicon crystal anisotropy is taken into account.