Abstract This paper describes mathematical and numerical models of thermal phenomena developed for computational analysis of the laser–arc hybrid welding process. The mathematical and numerical models were established to estimate temperature field and velocity field of melted material in the welding pool. Different heat source power distribution models for electric arc and laser beam, latent heat of fusion and latent heat of evaporation as well as buoyancy and liquid material flow through a porous medium were taken into consideration in the computational model. The results of computer simulation of laser–arc hybrid welding process, including temperature field and melted material velocity field, are presented in this study. The correctness of elaborated models is verified by experimental results.