Abstract: Dendritic growth in a binary mixture with imposed flow was investigated. When the Schmidt number was large, the asymptotic solution for the steady state was obtained by using the asymptotic analysis method. The zeroth-order and the first-order solutions are similar for the temperature and concentration fields. The shape of the dendrite is paraboloid of revolution on which there are small waves. The strength of external flow has a significant effect on the Peclet number of dendritic growth, the tip radius of den-drite and the tip growth velocity. For the given undercooling, the temperature at the dendritic tip or in front of the dendrite decreases with increasing flow, but the solute concentration increases.