In the present work, the resonance effects in the electromechanical drive system of a tissue paper machine are investigated. The drive consists of six D.C. motors. The inertia of the motors and the driven machines in conjunction with the shafts stiffness form mechanical resonators. Because of the harmonic content of the driving torque, resonance phenomena may be triggered which may lead to undesirable results. In this paper the investigation is focused on the Yankee and presses drive, where two threemass and one five-mass-system result. The use of elastic shafts with different stiffness (and damping) in the transmission system is studied. For the investigation of the resonance effects, a mathematical model algorithm was developed to be used for computer simulation via MATLAB / SIMULINK software, considering the inertia of the motors and driven machines, and the basic mechanical characteristics of the transmission shafts, i.e. the diameter, length, thickness, stiffness and damping.. Characteristic simulation results are presented. Considering the resonance effects analysis and simulation results, mechanical design guidelines can be given for the most significant drive components in order to avoid torsional oscillations resonance phenomena and minimize torsional oscillations in the drive system.