a body frame;

a rear swing arm swingably attached to the body frame via a pivot shaft;

an engine secured to the body frame; and

a power transmission mechanism which transmits a driving force from the engine to a rear wheel via a drive shaft and a damping device;

wherein the power transmission mechanism is configured such that:

a drive case incorporating a transmission mechanism is provided at a rear end of the rear swing arm, the transmission mechanism converting a direction of a driving force of the drive shaft and transmitting the driving force to the rear wheel;

the damping device which alleviates a shock applied to the rear wheel is provided in the drive case; and

a damping member is provided in the damping device so as to be coaxial with an axle of the rear wheel,

wherein the drive shaft is adapted to swing together with the rear swing arm, and

wherein the power transmission mechanism includes

a universal joint at a rear end of the drive shaft, so that the drive shaft and the universal joint are capable of sliding forwardly and rearwardly in an axial direction with respect to each other, and

a cover covering the universal joint, the cover extending forwardly from a drive case incorporating the power transmission mechanism.