Standard Solid-On-Solid models of crystal growth represent the appearance and disappearance of molecules on the crystal surface as stochastic events. Here, in order to model more realistically the growth of crystals from solution, we introduce a dynamic model of the uid in contact with the crystal surface and in this way account explicitly for mass transport in the solution. We present our hybrid model and establish its relation to standard SOS simulations while demonstrating explicit eects of mass transport that are usually ignored in SOS simulations. We then introduce flow in the solution in directions parallel to the crystal surface and observe dramatic eects on crystal growth for flows perpendicular to the step front as well as for flows parallel to the step. In order to understand the latter, quite unexpected feature, we study the effect of flow on isolated islands on a crystal surface and show that flow in the solution can induce spontaneous movement of 2D islands on the crystal surface.