A rotary damper for damping an impact by an upward opening door or a toilet seat by applying a braking force to it when it is closed, which develops a larger damping force than a conventional damper using a viscosity shear resistance when the door is closed, thus enabling the door to be opened with a light force, wherein there are provided an arc inelastic part (2e) ranging from one circular end edge (2c) to the other circular end edge (2d) of the tubular shaft part (2a) of a movable shaft (2) inserted rotatably into a casing (1) and an eccentric elastic part (2f) made in contact elastically with the inner peripheral surface (1a) of the casing (1) by bending it outwards from the one circular end edge (2c) to the other circular free end edge (2d) so that the eccentric amount becomes gradually larger than the radius of curvature of the inner peripheral surface (1a) of the casing (1), whereby, when the movable shaft (2) is closed in the arrow R1 direction by the rotation of the door, a frictional force against the inner peripheral surface (1a) of the eccentric elastic part (2f) becomes larger and, when the door is open in the arrow R2 direction, to the contrary, the frictional force can be reduced remarkably.