A sliding mode feedback algorithm is proposed to control the vibration of a flexible rotor supported by magnetic bearings. It is assumed that the number of states is greater than the number of sensors. A mathematical model of the rotor/magnetic bearing system is presented in terns of partial differential equations. These equations are then discretized into a finite number of ordinary differential equations through Galerkin's method. The sliding mode control law is designed to be robust to rotor unbalance and transient disturbances. A boundary layer is introduced around each sliding byperpiane to eliminate the chattering phenomenon. The results from numerical simulations are presented which not only corroborate the validity of the proposed controller, but also show the effects of various control parameters as a function of the angular speed of the rotor. In addition, results are presented that indicate how the current required by the magnetic bearings is affected by control parameters and the angular speed of the rotor.