A vibration proofing structure having a first base and a first oil damper mounted thereon having a first tank mounted on the first base, first pistons arranged in the first tank, and a first rod having a first end mounted on the first pistons and a second end outwardly extending from the first tank. The structure further includes a second oil damper including a second tank, second pistons arranged in the second tank and a second rod having a first end mounted on the second pistons and a second end outwardly extending from said second tank. A second base is provided on which the second end of the second rod is mounted. The first and second oil dampers are juxtaposed to each other and the first rod is connected to the second tank so as to permit the first and second oil dampers to rotate relative to each other.