To provide a vibration damping device which can surely damp axial and torsional vibrations and is easily assembled at a low cost.

This vibration damping device is constituted of first and second vibration damping parts assemblies 3, 4. The first vibration damping parts assembly 3 involves a first outer cylinder 31 which is inserted in the fitting hole of a cylinder block, an inner cylinder 32 inserted in the first outer cylinder 31 with a clearance between them, and a first vibration damping material 33 between the first outer cylinder 31 and inner cylinder 32. The second vibration damping parts assembly 4 involves a second outer cylinder 41 which is inserted in the hollow part of a fixed gear, an inner core 42 inserted in the second outer cylinder 41 with a clearance between them, and a second vibration damping material 43 between the second outer cylinder 41 and the inner core 42. The first and second vibration damping materials 33, 43 have damping characteristics which are appropriate for damping vibration in respective directions different from each other.