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The work concerns the mathematical and numerical modelling of the welding process using a laser beam heat source consisting of a single-mode core with a surrounding multi-mode ring. The numerical model of the heat source is developed based on the Gaussian distribution for both the core and the surrounding ring by using the results of experimental measurements of the beam power distribution. Thermal phenomena are analysed based on the governing equations of continuum mechanics: conservation of mass, momentum and energy. The model takes into account internal heat sources resulting from changes of material state. As a result of numerical calculations performed using the finite volume method and Chorin’s projection, temperature distributions and distributions of the velocity of liquid steel flow in the melting zone are obtained. The temperature distributions allowed for the estimation of the melted zone in the cross-section of welded joint and the heat affected zone. Welded joints obtained in the real laser welding (bead on plate) tests, which are carried out on steel sheets made of S355J2 steel with a thickness of 8 mm, are used to validate the obtained results. The research is conducted at Łukasiewicz Research Network – Institute of Welding, using the IPG MultiAxis laser welding station, which is equipped with a solid-state fiber laser pumped with semiconductor laser diodes. The active medium is an optical fiber doped with ytterbium (YLS - Yterbium Laser). It is a single-mode laser (SM) with two adjustable beam modes (AMB).