A three-dimensional numerical simulation for the travelling heater method growth of CdTe single crystals under an applied (vertical) static magnetic field was carried out. The effect of magnetic field intensity on the transport structures (fluid flow, concentration and temperature fields) in the liquid solution was investigated. The evolution of the growth and dissolution interfaces was taken into account. Numerical results show that the transport structures in the liquid solution exhibit three distinct behaviours at different field intensity levels. There is a critical magnetic field level, about 8.0 kG. below which the applied magnetic field is very beneficial, suppresses the convection and leads to more uniform concentration and temperature distributions and flatter growth interfaces for a prolonged and stable growth. It appears that the field intensity of 8.0 kG is the optimum level for which the convection was suppressed to a minimum and the growth interface was the flattest. At the field levels between 8.0 and 12.0 kG, the transport structures exhibit transitional behaviour; although the flow field is still stable, its intensity increases significantly and its patterns show asymmetric behaviour. The concentration distribution is also different, and the growth interface and isotherms become convex towards the solution, losing their flatness. At field levels higher than 12.0 kG, there are computational problems (convergence) in computing the concentration field, showing numerically unstable behaviour. The computed flow and temperature fields however indicate that the higher magnetic field levels may indeed lead to unstable transport structures in growth experiments. (C) 2003 Elsevier Science B.V. All rights reserved.