Recently the question on drilling rigs failures due to hidden oscillations was actively discussed. For instance, it was shown by the scientific group from Eindhoven University of Technology that such oscillations may appear in drilling rigs actuated by DC motor. In the works of the authors same effect was found for models of rigs with induction motor. Here a new mathematical model of a drilling rig activated by a salient pole synchronous motor is considered. Numerical modelling of the obtained model is performed.