The article justifies the application of explicitly defined static current and voltage characteristics in mathematical models of dynamic electric arc. The study involved the use of the generalised function approximating the above-named characteristics to create the differential and integral forms of the Novikov-Schellhase, Pentegov and Mayr-Pentegov mathematical models. Macromodels of arc were developed using the differential form of mathematical models and controlled voltage sources as well as using the integral form of models and controlled current sources. The effectiveness of macromodels was verified by means of simulations of processes in circuits with electric arc.