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An earlier model of deep-penetration laser welding has been simplified in order to provide a useful model of process analysis. This work involves the modelling of the various energy-absorption mechanisms which determine the keyhole shape and thus the dimensions of the melt pool. The penetration depth and weld width (top and bottom) predicted by the model are shown to be in close agreement with experimental results. The widening of the top of the weld seam as a result of Marangoni flow is accurately modelled by introducing an artificially enhanced value for the workpiece's thermal conductivity towards the top of the weld. The model allows analysis of the dependence of the weld profile on the process parameters.