Torsional vibrations must be considered in the design of all high-power drive-trains including an induction motor. Electromagnetic (EM) field in the air gap of an induction motor generates additional magnetic stiffness and damping between the rotor and stator. The inclusion of these magnetic effects is limited by the availability of simple and portable motor models. The main aim of this paper is to introduce a motor model including the speed and torque variation. The presented model is based on the linearization of the common space-vector models of induction motors. The parameters of this model are identified for the rated operating condition. This motor model can be extended to include variable speed and torque operation. The numerical results demonstrate that this model describes accurately the magnetic effects over the large speed and torque range. In addition, the numerical results demonstrate the significance of magnetic stiffness and damping in variable speed motor-driven compressors with a soft coupling.