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International audience; This paper focuses on the vortex formation effect during the application of a laser-fusion cutting technique. This industrial technique is typically associated with the ejection of a film of molten stainless steel blown off by a subsonic laminar jet of nitrogen gas used to assist the process. Without taking into account the transverse movement of the workpiece, we consider a 4 mm thick stainless steel plate. The resulting molten metal flow is assumed to be laminar, steady, viscous and incompressible. The numerical results reveal vortex structures adjacent to the walls at the entrance of the kerf, and a pair of eddies outside the kerf. Remarkably, these vortex structures can produce a separation point in the molten film, and thereby they can affect the surface quality of the processed material. The problem is investigated in the framework of a numerical technique available in the Fluent software, based on a volume of fluid (VOF) surface-tracking strategy and the enthalpy method to account for material solidification or melting.