A bicycle designed to reduce the transfer of vibrations to the rider. The bicycle includes a seatpost assembly comprising an inner member, an outer member at least partially surrounding a portion of the inner member, and a damping member disposed between the inner member and the outer member. The damping member provides vibration damping between the frame and the seat. Preferably, the inner member includes a necked portion positioned within the damping member. In addition, the damping member can include a body portion positioned inside the outer member and a head portion positioned longitudinally adjacent the outer member. The concepts of the present invention are also applicable to frame members of the bicycle frame, such as the chainstays, the seatstays, and the fork.