The model for anisotropic crystal growth on a substrate covered by a mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase is developed. The model assumes that surface diffusion and deposition flux are the main mechanisms of the growth, and that the three key surface quantities (energy, mobility and adatom diffusivity) are anisotropic with either four- or six-fold symmetry. A geometrical approach to the motion of crystal surface in two dimensions is adopted and nonlinear evolution equations are solved by a finite-difference method. The model allows the direct computation of the crystal surface shape and the study of effects due to finite mask thickness. As in experiments, lateral overgrowth of crystal onto the mask is found, as well as comparable crystal shapes; the anisotropy of the surface mobility is found to play the dominant role in the shape selection. The amount of the overgrowth and the shapes can be effectively controlled by orienting the fast and slow growth directions with respect to the substrate. (C) 2002 Elsevier Science B.V. All rights reserved.