The problem of simulation of the arc-suppression process in the case of switching off high-current dc circuits by devices with a liquid–metal working medium is considered. Since devices with a liquid–metal contact are designed to switch specific power circuits, the possibility of joint consideration of the electrical circuit and the switch is used to optimize the shutdown process. The obtained mathematical model allows with the use of the known temperature profile of the dynamic arc to calculate the main dynamic characteristics of the arc discharge, such as current, voltage, conductivity, temperature, and the trunk conductor radius. It is shown that, if the real temperature profile of the arc is not known, calculation of such integral characteristics of the arc-suppression process as current, resistance and intensity of the arc trunk can be carried out with the use of an equivalent temperature profile. On the basis of the obtained mathematical model, a calculation methodology is developed for the process of circuitry cutout by an apparatus with liquid–metal contacts with a change in the topological structure of the circuit being switched off during the commutation process.