This work presents a numerical investigation of the undesired lateral vibrations (whirling) occurring in drill-strings, which is one of the main sources of losses in drilling applications. The numerical studies are conducted using a nonsmooth lumped parameter model, which has been calibrated based on a realistic experimental drilling rig. The numerical investigations are focused on identifying different types of whirling responses, including periodic and chaotic behavior, which have been previously observed experimentally. As a result, the parameter space is divided into different regions showing dynamically relevant responses of the model, with special interest on the influence of the mass and angular velocity of the drill-string system. In particular, the study reveals the coexistence of various types of whirling motion for a given set of parameters and their sensitivity to initial conditions. The obtained theoretical predictions confirm previous experimental studies carried out by the authors, which provides a solid basis for a better understanding of whirling phenomena in drill-string applications.