In this article results of numerical simulation done based one the real experiments input of S700MC steel laser and hybrid welding were presented. Differences in the process thermal cycles of both mentioned technologies cause different distortions and stresses distribution. Numerical analyzes carried out in the SYSWELD software made it possible to understand both the influence of thermal cycles of used methods on the distributions of temperature fields and individual metallurgical phases, as well as the distribution of stresses and strains arising as a result of their interaction. The results of the analysis allowed to determine both the differences in the stress values and the method of their distribution, which is often much more important from the point of view of the exploitation of welded joints. An additional aim of this paper is to propose a mathematical description of the computational model that is usable for simulation computations of welding processes. The benefits resulting from the use of such analyzes have also been indicated due to the significant savings in time and resources to be spent on the development of correct technologies for combining modern construction materials such as thermomechanically treated steels.