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One of the most intensively studied lasers are diode pumped Yb:YAG lasers. Issues concerning the use of this type of solid state lasers in the industry are under particular investigations in the field of experimental research as well as theoretical study. The major factor determining the temperature field in the laser beam processing is the beam power and its distribution in heated element as well as liquid material motion in the fusion zone wen the laser beam melts heated material. This work concerns mathematical and numerical modelling of temperature field during Yb:YAG laser heating of sheets made of S355 steel with the motion of liquid steel in the fusion zone taken into account. Laser power distribution and the caustics are determined on the basis of the geostatistical kriging method. Temperature field and melted material velocity field in the fusion zone are obtained from the numerical solution of continuum mechanics equations using projection method and finite volume method. Numerical algorithms are implemented into computer solver using ObjectPascal programming language. Computer simulations of Yb:YAG laser heating process are performed for different process parameters. Characteristic zones of experimentally obtained cross sections of heated elements are compared to numerically predicted fusion zone and heat affected zone.