Electric drive trains have a torsional rigid-body vibration mode at a small, nonzero frequency. If an excitation occurs close to this frequency, the vibration amplitude may grow large and the electrical machine may suffer from significant additional losses. Standards set constraints on the oscillating torque in the shaft coupling and on the harmonics of line current. They indirectly limit the vibration amplitude and losses of the machines. Time-discretized finite-element analysis was used to study the losses of six induction and six synchronous machines under torsional vibration restricted by the constraints above. All the machines were supplied from sinusoidal voltage sources. In the worst cases of the induction motors, the vibration increased the electromagnetic total loss by about 20%. The constraints on synchronous machines are milder than those for induction machines. In this case, the maximum increase of the loss was 75%. The limit on the harmonic currents is essential from the loss point of view. Without this limit, the additional loss at the rigid-body resonance would lead to a temperature rise high enough to destroy the insulation system of the machine. The method of loss analysis was validated by measured results.