A shock-absorbing stopper comprising: a cylindrical elastic body , to a fixed-side end portion of which a fixed-side metal fitting is connected and to a movable-side end portion of which a movable-side metal fitting is connected and which has an annular hollow in an outer peripheral surface of the cylindrical elastic body , wherein the shock-absorbing stopper is sectioned into three portions by the hollow of a small diameter portion formed by the hollow , a fixed-side large diameter portion located closer to a fixed side relative to the hollow , and a movable-side large diameter portion located closer to a movable side relative to the hollow , an outer diameter dimension (Φd 2 ) of the movable-side large diameter portion is set smaller than an outer diameter dimension (Φd 1 ) of the fixed-side large diameter portion , and an axial width (w 2 ) of the movable-side large diameter portion is set smaller than an axial width (w 1 ) of the fixed-side large diameter portion , wherein the outer peripheral surface of the small diameter portion , the fixed-side large diameter portion and the movable-side large diameter portion at the elastic body is configured to be radially outward swollen and deformed when the elastic body is compressed by a load applied to the movable-side metal fitting , whereby the movable-side end portion is displaced in a direction approaching the fixed-side end portion , an outer diameter dimension of the small diameter portion is set smaller than the outer diameter dimension (Φd 1 ) of the fixed-side large diameter portion and the outer diameter dimension (Φd 2 ) of the movable-side large diameter portion , the axial width (w 2 ) of the movable-side large diameter portion is set only by an axial width (w 3 ) of the movable-side metal fitting , and an axial width (w 4 ) between the hollow in the elastic body and the movable-side metal fitting is set to zero. a cylindrical elastic body , to a fixed-side end portion of which a fixed-side metal fitting is connected and to a movable-side end portion of which a movable-side metal fitting is connected and which has an annular hollow in an outer peripheral surface of the cylindrical elastic body , wherein the shock-absorbing stopper is sectioned into three portions by the hollow of a small diameter portion formed by the hollow , a fixed-side large diameter portion located closer to a fixed side relative to the hollow , and a movable-side large diameter portion located closer to a movable side relative to the hollow , an outer diameter dimension (Φd 2 ) of the movable-side large diameter portion is set smaller than an outer diameter dimension (Φd 1 ) of the fixed-side large diameter portion , and an axial width (w 2 ) of the movable-side large diameter portion is set smaller than an axial width (w 1 ) of the fixed-side large diameter portion , wherein the outer peripheral surface of the small diameter portion , the fixed-side large diameter portion and the movable-side large diameter portion at the elastic body is configured to be radially outward swollen and deformed when the elastic body is compressed by a load applied to the movable-side metal fitting , whereby the movable-side end portion is displaced in a direction approaching the fixed-side end portion , an outer diameter dimension of the small diameter portion is set smaller than the outer diameter dimension (Φd 1 ) of the fixed-side large diameter portion and the outer diameter dimension (Φd 2 ) of the movable-side large diameter portion , the axial width (w 2 ) of the movable-side large diameter portion is set only by an axial width (w 3 ) of the movable-side metal fitting , and an axial width (w 4 ) between the hollow in the elastic body and the movable-side metal fitting is set to zero. <EOS>