A rear cushion unit has an upper end mounted on a swing arm and a lower end coupled to pivot brackets in a position below a pivot shaft. The pivot brackets are independent of each other and are not coupled to each other. With the above construction, a fuel tank, electric parts, or other parts, for example, can be clustered between the left and right brackets. Accordingly, the parts can be disposed near the center of gravity of the vehicle body. Therefore, the maneuvering capability of racing and off-road vehicles incorporating such an arrangement can be increased. The vehicle frame can be simplified in structure and can be manufactured at a reduced cost. When the vehicle is assembled, the distance that the worker needs to move can be reduced, and hence the productivity of the vehicle is increased. The size of the vehicle is reduced because of the clustered arrangement of the parts.