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Research efforts are underway to model and study the dynamics of a drill string, and preliminary results are presented in this work. The dynamics of a drill string system has non-smooth characteristics. Moreover, the drill string system dynamics exhibits qualitative changes with respect to the rotation speed of the drill string and friction coefficients associated with the contact between the drill string and the outer shell and the drill string and the well bottom. The coupling between torsion, lateral, and axial vibrations and the nonlinear interactions between them need to be investigated to better understand the dynamic behavior of the drill string system. As a preliminary step towards understanding the dynamics of the drill string, four-degree-of-freedom models are developed for the system by using two rotating sections: an inner stator that can undergo radial displacements and an outer rotor. Stickslip interactions between the drill string and the outer shell are also considered in the model development. Two sets of differential equations are obtained for the system by using displacements and momenta as system states in one model and displacements and velocities as system states in another model. For different values of friction coefficients, rotation speeds, and rotation torques, the results obtained by using the developed models are presented, discussed, and compared with experimental results.