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A numerical framework for simulation of the steady-state thermal behaviour in keyhole mode welding has been developed. It is based on the equivalent heat source concept and consists of two parts: computational thermo-fluid dynamics and heat conduction. The solution of the thermo-fluid dynamics problem by the finite element method for a bounded domain results in a weld pool interface geometry being the input data for a subsequent heat conduction problem solved for a workpiece by a proposed boundary element method. The main physical phenomena, such as keyhole shape, thermo-capillary and natural convection and temperature-dependent material properties are taken into consideration. The developed technique is applied to complete-penetration keyhole laser beam welding of a 15 mm thick low-alloyed steel plate at a welding speed of 33 mm/s and a laser power of 18 kW. The fluid flow of the molten metal has a strong influence on the weld pool geometry. The thermo-capillary convection is responsible for an increase of the weld pool size near the plate surfaces and a bulge formation near the plate middle plane. The numerical and experimental molten pools, cross-sectional weld dimensions and thermal cycles of the heat affected zone are in close agreement.