A composite resilient mount for rolling element bearings, comprising a composite hoop portion, and including a plurality of circumferentially dispersed inner pads and outer pads defining a plurality of arcuate beam portions disposed circumferentially between adjacent pads. The hoop portion and the inner and outer pads, may comprise a circumferentially wound fiber, such as a carbon fiber, and a resin. The inner and outer pads may be rounded, feathered or otherwise configured to eliminate edges from the inner and outer pads, thereby preventing damage to adjacent components. A method for providing damping to a rolling element bearing is also disclosed.