A structure for installing a rear cushion in a motorcycle having a hydraulic shock absorber with a subsidiary cylinder used as the suspension device. The rear swing arm includes a pair of left and right arm portions, the respective front portions being coupled with a first cross member and a second cross member. A pair of cushion brackets extend in the back-and-forth direction with the upper portion of the rear cushion sandwiched therebetween. The front and rear ends of the cushion brackets are coupled to the first and second cross members, thereby supporting the cushion brackets at both ends. An upper portion of the rear cushion fits within a space enclosed by the first and the second cross members, and the left and right cushion brackets, and is coupled to the intermediate portion of the left and right cushion brackets.