A squeeze film damper for a bearing and a vibration damping mechanism capable of damping the vibration of a rolling bearing are provided. The squeeze film damper is small in construction and can be easily made by mass production. The vibration damping mechanism is capable of damping both radial and axial vibrations. A bearing housing 15 is provided with a bearing holding bore 16 of a diameter greater than the outside diameter of the outer ring 14 of a bearing, and an oil hole 19 through which oil is supplied into the bearing holding bore 16. A vibration damping mechanism 1 is formed by inserting a thin, flat sheet 17 provided with slits into an annular space formed between the inner wall of the bearing holding bore 16 and the outside surface of a bearing held in the bearing holding bore 16 so as to surround the bearing. Parts of the thin, flat sheet extending between the adjacent slits serve as elastic beams. The elastic beams center the bearing and support the centered bearing elastically. The vibration of the bearing is damped by the squeeze film effect of an oil film formed by supplying oil into the annular space.