This study investigates the effect of constant axial torque on the dynamics of rotorbearing systems using a finite element model. The finite element equation of motion is formulated using the variational approach and the inclusion of axial torques gives rise to an incremental torsional stiffness matrix. This matrix is circulatory since the system is non-conservative. The finite element model is used to determine the static buckling torques and the critical speeds of a uniform shaft for short and long bearings.