An apparatus for damping of a flywheel, which is configured so that a second mass may rotate in a direction for offsetting torsional vibration of an engine transmitted to a first mass through a damping spring. The apparatus includes: guides disposed between damping springs and guiding the damping springs extending/contracting in a rotational direction by a damping operation; and a third mass arranged coaxially with the second mass, with one end connected to the guide, and relatively rotating in a direction for offsetting torsional vibration of the engine transmitted to the second mass.