A three-dimensional numerical simulation for the liquid phase electroepitaxial growth of GaAs under a vertical stationary magnetic field was carried out. The effect of magnetic field intensity and non-uniformity on the flow field in the liquid solution was investigated. Numerical results show that the flow patterns exhibit three distinct stability characteristics: a stable flow field up to a magnetic field level of Ha = 150, a transitional flow between Ha = 150 and 220, and an unstable flow above Ha = 220. In the stable region, the applied magnetic field suppresses the flow field, and the flow intensity decreases with increasing magnetic field exhibiting a power law of U-max proportional to Ha(-5/4) relationship for the maximum velocity (U-max). In the transitional region, the flow intensity increases dramatically with the increase in magnetic field strength. The flow patterns are significantly different from those in the stable region. The flow field is no longer axisymmetric but still stable. In the unstable region, the flow structure and intensity change with time. Under a strong magnetic field, the flow cells are confined to the vicinity of the vertical wall and exhibit significant non-uniformity near the growth interface. Such strong flow fluctuations and non-uniformities near the growth interface may have an adverse effect on the growth process and lead to an unsatisfactory growth. In this region, the maximum velocity (U-max) obeys approximately a power law U-max proportional to Ha(5/2). Results show that for a successful growth the effect of applied magnetic field must be optimized. (C) 2002 Elsevier Science B.V. All rights reserved.