A screw compressor utilizing radial and axial or thrust bearings to maintain the position of the rotors radially and axially and utilizing a damping fluid to dampen rotor vibrations. The damping fluid may conveniently be provided in the form of lubricant that is already used in the compressor to seal the clearances between the rotors and between the rotors and the cylinder during compression. The damping fluid is included in a squeeze film damper, arranged in a parallel arrangement with the radial or thrust bearings, which provides viscous damping to the rotor. The introduction of additional viscous damping such as may be provided by squeeze film dampers may result in significant reduction of compressor vibration regardless of the source of vibration.