The step-wise model of displacement of the arc spot in cold electrode arc heaters is considered in this report. We have shown theoretically that the nature of the motion of the arc spot substantially influences the erosion: the step-wise motion of the spot leads to the increase in the erosion in comparison with the continuous motion, the greater it is, the greater the length of the arc step. We compared both models to the same experimental results for copper cathode in air. The step-wise model shows somewhat better agreement to our experimental erosion data, than the continuous one. In order to access the validity of the step-wise model we used results for electric discharge machining experiments. A good agreement was also obtained.