Nowadays, operational on-off switching of power units and facilities with a large amount of supply current is performed by using vacuum circuit breakers (VCB). The main disadvantages of these vacuum circuit breakers are the characteristics of switching transients linked with repeated breakdowns of arc gaps and voltage escalation. They arise due to occurrence of current cut-off and virtual current cut-off during switching of unloaded and loaded furnace transformers (FT). These overvoltages can have a negative effect on the insulation of transformers windings and suitable cable lines. In this paper, the well-known mathematical models of burning electric arc in vacuum were analyzed. Transient recordings of experimental overvoltage studies during switching of vacuum circuit breakers were carried out for analysis and comparison. The main differences between the models are highlighted, as well as differences in relation to actual transients. Based on the results of the evaluation of the mathematical models of the arc, a new more complete model was developed. The model includes additional dependencies of several factors to reveal the complete picture in case of burning arc in the VCB arc gaps.