A Monte Carlo model is used to simulate the morphological evolution of crystals growing under the influence of a uniform drift in the nutrient phase. The model combines nutrient transport (via a biased random walk) with anisotropic surface attachment kinetics and surface diffusion. It is found that the crystal morphology closely depends upon the imposed drift, growth temperature (or bond strength), and supersaturation. Facets facing the drift direction exhibit enhanced morphological stability as compared with the no-drift situation. © 1989 The American Physical Society.