Studies on modeling and simulation of arc help to choose arc-extinction methods and line-selection methods in distribution network. Four kinds of arc mathematical equations are given such as Cassie, Mayr, Schwarz and the cybernetic model. Mayr, Schwarz and the cybernetic model are suitable for describing the arc characteristics when the grounding current is small. The arc model of Schwarz and the cybernetics is established, and these two models are compared using a test circuit of arc characteristics. The cybernetic model can set arc length, reflect the arc fault conditions and apply to simulation of single-phase arc grounding fault in resonant earthed system. The resonance earthed system model and the cybernetic model are established by ATP-EMTP, and the effect of arc length on arc impedance, steady and transient arc characteristics is analyzed. The results show that the cybernetic model is more intuitive and accurate to simulate arc grounding fault in resonant earthed system.