To form a soft layer of a base-isolation bearing structure by vulcanizing a rubber composition in which a resin obtained by hydrogenating a copolymer of a cyclopentadiene-based monomer and a styrene-based monomer is blended at a predetermined pts.wt. or lower with a base rubber.

A base-isolation bearing body M comprises a soft layer 2 having a plurality of sheets laminated alternately between two sheets of disc-shaped coupling flanges 1, 1, a constraint layer 3 and a cover layer 4. The coupling flange 1 and the constraint layer 3 are formed of a material having rigidity such as steel plate. The soft layer 2 is formed by vulcanizing a rubber composition in which at most 100 pts.wt. of a resin obtained by hydrogenating a copolymer of a cyclopentadiene-based monomer and styrene-based monomer is blended with 100 pts.wt. of unvulcanized base rubber. The basic rubber material is to be natural rubber or the like. Further, a vulcanizer, vulcanization accelerator or the like is added adequately to the rubber composition. By this process, a rubber composition which does not increase adhesion and is excellent workability can be obtained, thereby a soft layer having a high deformation performance can be obtained.