The cutting stability and the lifetime of High Speed Machining spindles highly depend on its modal behavior. A specific electromagnetic excitation device is used to measure the Frequency Response Function of the spindle at high speeds. The evolution with speed of the eigenfrequencies and of the radial stiffness is analyzed. A numerical model is developed to obtain the associated modes shapes; since they cannot be measured experimentally. The simulations, which are in good agreement with the experiments, enable an understanding of the evolutions of the spindle dynamic, and notably of the evolution of modal coupling at high speed.