Numerical modelling of laser welding requires that numerous strongly coupled physical phenomena be taken into account. A laser is a source of welding heat characterized by the small size of the heating volume and the shape of the fusion zone has a marked impact on the quality of the weld. In this work, a conical heat source was used with geometrical parameters to give the appropriate profile of the fusion line. The use of the weld shape factor and the dependence of the power density on the linear welding energy increases the accuracy of matching the calculated shape of the fusion line. The heat source was tested for the continuous welding case of a sheet made of steel type S355J2. The CFD software ANSYS Fluent was used to calculate the welding model. The temperature field, calculated using the finite volume method, was used to calculate the phase composition and fusion zone profile tracking. The nodes of the model reaching the maximum solidus temperature of S355J2 steel, form the profile of the fusion zone. The laser welding model allows for tracking of the kinetics of phase transformations in the cooling stage. Continuous cooling transformation phase diagram data is loaded for the welded steel grade. The calculation results of the welding model were compared with the weld micrographs.