Abstract: An apparatus for damping a plurality of vibrations applicable to an apparatus for mounting a vehicular engine on a vehicle body. The apparatus comprises: (a) a first block; (b) a second block; (c) a block member for damping first vibrations having high frequencies and having large amplitudes, the first vibrations being generated and transmitted from the first block to the second block; and (d) at least one viscous shearing force resistance generator for damping second vibrations having low frequencies and large amplitudes, the second vibrations being generated and transmitted from the first block to the second block and from the second block to the first block. The viscous shearing force resistance generator is formed within the block member. The viscous shearing force resistance generator, e.g.