The article presents reasons for nonlinear static voltage-current characteristics of an electric arc; the characteristics consist of an initial voltage drop followed by a voltage rise in the range of strong currents. The article suggests that overcoming difficulties in mathematical modelling of electric processes in circuits with arcs requires the use of Pentegov assumptions and the building of an arc model utilising a static hyperbolic-linear characteristic. The article also presents a method for the experimental determination of arc model parameters with sinusoidal excitation as well as describes a macromodel built using the MATLAB-­Simulink programme. The correctness of analytical expressions specifying mathematical model parameters was verified through simulation. The study also involved testing the resistance of the proposed method to arc length random disturbances.