Circuit breakers are a significant part in switchyard protection. One of the most possible classifications of breakers is through arc-extinguishing mediums. The irreplaceable medium of today in the middle-voltage breakers is a vacuum, which at the same time is more and more present at the high-voltage area. In this thesis, the emergence of an electric arc is described as well as the electrical contacts between which the arc appears. It's important to know the possibilities for extinguishing the electrical arc and preventing its reignition so it doesn't come to damage to the equipment or the injuries of employees. For the purpose of examining the electric arc, the most common applications are completed mathematical models. They represent the set of blocks that are described with differential equations and they make an extension of the software package MATLAB/SIMULINK. Further to, simulations are presented for the cases of terminal and short circuit fault. Obtained graphical results of simulations were used for voltages and currents comparison during the reignition and extinguishing of an electrical arc. Simulations are performed for different electric arc models, and all the results are presented in the annex along with the table for every related model.