The vibration damping system, especially for use in the damping of vibrations e.g. from trains, tramcars, other traffic and damping of ground borne vibrations in general, comprises an anti-vibration plate in the form of a plate having a first and a second major surface. The anti-vibration plate comprises mineral fibers, a non-foamed polymeric material and/or a polymeric foam. The anti-vibration plate can further be provided with one or more hollow spaces, i.e. cavities. The anti-vibration plate is obtainable by a method comprising the step of subjecting an area of the opposite surface of the plate to a compression treatment in one or more steps, which compression treatment is sufficient to reduce the static and/or dynamic stiffness of the plate.