This paper derives the analytical characterization of Maxwell radial vibrations due to saturation effects in induction machines, and especially in traction motors. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the stator and rotor slot numbers, and stator natural frequencies, these forces can be responsible for high magnetic noise levels during electrical starting and braking. A simple rule to avoid saturation magnetic noise is then proposed, and applied to an industrial motor. A fully analytical model of the motor vibro-acoustic behavior, including saturation effects, is finally presented. Simulation results show that the new proposed motor improves magnetic noise level up to 20 dB, whereas experiments give a 15 dB improvement.