We investigate the stabilizing effects of a constant vertical magnetic field on the flow in a heated planar liquid metal layer. The steady shear flow driven in the bounded layer by the imposed horizontal temperature gradient can involve two types of instability: stationary transverse instabilities and oscillatory longitudinal instabilities. The performed approximate analytical linear stability analysis shows that the vertical magnetic field has a great stabilizing effect on both types of instability with variations of the thresholds (critical Grashof numbers) as Gr(c) - Gr(c)(Ha = 0) infinity Ha(2) for the longitudinal instabilities and as Gr(c) infinity exp(Ha(2)/21.6) for the transverse instabilities (Ha is the Hartmann number proportional to the intensity of the magnetic field). Both instabilities also disappear beyond a limit value of Ha. These results could be of great interest for crystal growers as the vertical field is seen to delay the onset of instabilities, in particular the oscillatory instabilities which are responsible for the appearance of undesirable striations in the grown crystals. (C) 2002 Elsevier Science B.V. All rights reserved.