In this article, reduced-order models of a drill-string system are developed, the predictions of these models are studied, and qualitative comparisons are made with experimental studies. The reduced-order models allow for radial, bending, and torsion motions of a flexible drill string and stick-slip interactions between the drill string and an outer shell. Qualitative changes in the system motions are studied with respect to the rotation speed of the drill string and the friction coefficient between the drill string and the outer shell. The nonlinear motions predicted by the model are in agreement with the experimental observations, and these studies suggest that there may be preferred friction coefficient values for which most of the drill-string motions occur close to the center of a borehole. These modeling and experimental studies can serve as an important basis for furthering our understanding of drill-string dynamics and schemes for controlling them.