A multi-physics numerical model was developed to investigate the influence of a steady magnetic field aligned perpendicular to the welding direction during partial penetration high power laser beam welding of aluminium in downhand position. Three-dimensional heat transfer, fluid dynamics including phase transition and electromagnetic field partial differential equations were successfully solved with the finite element differential equation solver COMSOL Multiphysics 4.2. The implemented material model used temperature-dependent properties up to evaporation temperature. Marangoni convection in the surface region of the weld pool, natural convection due to the gravitational field and latent heat of solid-liquid phase transition were taken into account. Solidification was modelled by the Carman-Kozeny equation for porous media morphology. The flow pattern in the melt as well as the weld bead geometry were significantly changed by the induced Lorentz force distribution in the liquid metal. It reveals that the application of a steady magnetic field to laser beam welding with corresponding Hartmann numbers Ha(2) approximate to 10(4) allows for a suppression of the characteristic wineglass-shape of the weld cross section caused by thermocapillary flow. The numerical results are in good agreement with experimental results obtained with welding of AlMg3 with a 16 kW disc laser. The steady magnetic field was delivered by permanent magnets mounted on both lateral sides of the weld specimen. The maximum magnetic flux density was around 500 mT. It shows, that the applied magnetic field has a predominant dissipating effect on the weld pool dynamics independently of its polarity. (C) 2013 Elsevier Ltd. All rights reserved.