The effect of a magnetic field on the onset of instabilities is studied numerically in flow situations typical of horizontal Bridgman configurations. These situations are characterized by a buoyant convection due to a horizontal temperature gradient. Different laws of variation as a function of the intensity of the magnetic field have been found for the thresholds, from exponential increases to clear decreases, depending on the geometry of the configuration (extended layer, transversally confined layer, 3D cavity), the type of instability, the orientation of the magnetic field. Energy budgets at the thresholds have shown that, in most cases, the variations observed are connected to changes in the spatial distribution of the dominant destabilizing shear term. (C) 2007 Elsevier B.V. All rights reserved.