A 3D model of a hollow cathode of a thermal plasma torch was developed to study the motion of the electric arc in the upstream part as well as its influence on the characteristics of the thermal plasma generated at the entrance of the downstream part (anode). The translational motion along the axis and the rotational velocity of the cathodic arc root are studied. The results of the model are presented and compared with those of the literature and also with experimental results. Good agreements on the prediction of the axial arc position and of the rotational speed of the arc root are found with the literature. A correlation is also shown between the theoretical positions of the arc root and the experimental traces of erosion observed on the cathode.