The interaction between convection and dendritic growth has been a subject of great interest in the area of material science for many years. The experimental observations have shown that convective motion in liquid may have a significant effect on dendritic growth, changing the growth velocity of the tip and the micro-structure pattern. The convective flow, in different cases, may be measured by the Reynolds number, Grashof number, or the parameter of density change during phase transition. In this paper, I shall discuss the effect of convective flow on steady axisymmetric dendritic growth from an undercooled pure melt and summarize the linear stability criterion for several typical cases. (c) 2006 Elsevier B.V. All rights reserved.