A self-leveling viscous elastic damper comprising an inner member at least partially received in an outer member and joined to the outer member with an elastomeric shear spring. A main fluid chamber is included in the outer member in communication with a second fluid chamber in the inner member through restricted orifice means. A third fluid chamber, separated from the main fluid chamber by a partitioning wall, is also included in the outer member. An elastomeric bladder for selective gas pressurization is disposed in the second fluid chamber. An elastomeric gas accumulator for selective gas pressurization is disposed in the third fluid chamber. Pump means extend through the partitioning wall for pumping fluid from the third fluid chamber to the main fluid chamber. An elastomeric diaphragm in the main fluid chamber connects the pump means to a peripheral wall of the outer member.