PURPOSE: To prevent the length more than required amount of threading allowance of a piston rod for a cylinder attached to the upper support of a suspension device used by applying preload to an elastic body.

CONSTITUTION: A cylindrical part 16a is pressedly fitted to the upper end periphery of an inner cylinder member 13 by pressing a rebound plate 16 whose lower face is provided with the cylindrical part 16a to fit to the upper end of the inner cylinder member onto the upper end of the inner cylinder member in the outer cylinder member 12 and the inner cylinder member 13 which are connected through an elastic body 14. The elastic body 14 is thereby compressedly deformed, and art upper support 11 remaining in such a state as it is therefore obtained. The piston rod 7 of a suspension device is inserted in the inner cylinder member 13 of the upper support and fixed with nuts, and the suspension device can therefore be attached by attaching the outer cylinder member to a car body.