To simultaneously attain remarkable increase in pinch spring force and suppress increase in radial dynamic spring force by arranging space portions on an axially intermediate portion of a device between a rubber member and an outer cylinder, vulcanizingly connecting the rubber member to an inner cylinder, and then fixing the rubber member to an outer cylinder.

Upper and lower spaces S are formed on an axially intermediate portion of a rubber member 3, so as to be recessed in an outer peripheral direction. Bilateral projections P are formed between the spaces S on an axially intermediate portion, so as to be projected in a radial direction. After the rubber member 3 is vulcanizingly connected to an inner cylinder 1, resin-derived adhesive is applied onto the whole of outer peripheral surface of the rubber member 3 or the whole of an inner peripheral surface of an outer cylinder 2 corresponding to the rubber member 3, for fixing the rubber member 3 to the outer cylinder 2. It is thus possible to simultaneously attain remarkable increase of pinch spring force and suppress increase of dynamic spring force. It is also possible to remarkably improve durability.