A successful oil and gas prospecting requires many efforts to overcome the encountered challenges, some of these challenges include drill string axial, lateral and torsional vibrations. These phenomena may cause premature component failures of the drilling system, dysfunction of measurement equipments, and increase time and costs of the prospecting process. Torsional vibrations are present in most drilling processes and may reach a severe state: stick-slip. An improved understanding about the stick-slip phenomenon provides tools to avoid the increase of prospecting time and costs, assuring the investment and success of the drilling process. Firstly, a numerical analysis of the drill string is performed with different friction models. These models are proposed in order to get familiar with the drill string dynamics. Also, it is described the experimental procedure with a nonlinear friction aiming to induce stick-slip and is performed a simple analytical modeling of the problem. The friction model is based on dry friction imposed by a break device. The nonlinear behavior of the experimental apparatus is analyzed and the numerical model is validated comparing experimental and numerical bifurcation diagrams.