The present invention is a bicycle including a bicycle frame and a rear wheel suspension system that is attached to the frame. The rear wheel suspension system includes a rear wheel swingarm and a shock absorber that is engaged to the swingarm to control the motion of a rear wheel of the bicycle. A change in the vertical wheel travel (.DELTA.VWT) of the rear wheel is related to a change in the length of the shock absorber (.DELTA.SL), providing a shock rate (SR) according to the relationship: SR=.DELTA.SL/.DELTA.VWT. The shock rate (SR) changes throughout the vertical wheel travel of the rear wheel, such that the change in the shock rate dSR/dVWT has a change in sign as the rear wheel travels through its vertical wheel travel. The shock rate may at first decrease in value and subsequently increase, or initially increase in value and subsequently decrease throughout the vertical wheel travel of the rear wheel. In various exemplary embodiments the swingarm may be attached to the frame at a single pivot point or through a linkage system.