Embodiments of the present invention are directed to apparatus and methods of attenuating vibration, particularly for modern stepper machines and other types of vibration sensitive equipment. The attenuation system exhibits good vibration attenuation in the axial or support direction, and exhibits low or substantially zero lateral stiffness to prevent transmission of any vibrations between any of various portions of the machine. In one embodiment, an apparatus for attenuating transmission of lateral vibration between a first mass and a second mass comprises a vibration attenuation device including at least one bellows oriented along a support axis. The at least one bellows is connected between the first mass and the second mass and has an interior volume pressurized with a fluid to an internal fluid pressure which is greater than a zero-stiffness pressure such that the vibration attenuation device exhibits a negative lateral stiffness. A positive stiffness device is coupled between the first mass and the second mass. The positive stiffness device has a positive lateral stiffness which may be substantially equal to or greater than the negative lateral stiffness in magnitude.