The urgency of the discussed issue is caused by the necessi ty of applying different types of switching and principles of construction of switching devices, performing multiple tripping in DC circuits with inductive load. The main aim of the study: to justify the use of the proposed model contactless switch in DC circuits with inductive load performing arcless switching. The methods used in the study: a mathematical model for calculating the transition process, which allows calculating the current in high-current circuit of the used parameters of contactless switch. The results: the authors introduced the model of contactless switch in DC circuits with inductive load. A mathematical model for calculating the transients by the method of state variables has been developed. It allows calculating the current in the load circuit using parameters of contactless switch. The authors held as well the mathematical and the virtual modeling of operation of the model with the given parameters of contactless switch.