During the drilling operations of an oil well, drilling columns are subjected to dynamic actions, thus suffering vibrations. Such vibrations when uncontrolled can cause early fatigue of the material, damage to drills or even the breaking of the column. Phenomena such as Bit Bounce, Stick-Slip and Forward / Backward Whril, which arise from axial, torsional and lateral vibrations respectively, are the subject of several studies. This work analyzes the torsional dynamics of a vertical drilling column considering dry friction between the drill and the soil. It is considered that the top of the column has a constant speed imposed by an engine and the base is subject to torque due to the presence of dry friction. Because of this friction, the resulting movement of the column can be characterized by two qualitatively different modes, the stick mode and the slip mode, with an abrupt transition. The dynamics of the column is modeled using the axis theory to then be discretized by finite elements. Matlab programs were developed for numerical simulations.