A suspension assembly for a bicycle frame which elastically supports a rear frame member, which in turn rotatably supports the rear wheel. Preferably, the frame is a two-piece construction with the suspension assembly interconnecting the rear frame to the main frame. The suspension assembly is positioned around the bottom bracket such that the rear frame member pivots about the axis of the bicycle crank axle of the bottom bracket. This arrangement allows the rear wheel and rear frame member to move relative to the main frame, without any adverse affects to the drive train assembly. In the preferred embodiments, drive train assembly can be either a chain drive or a shaft drive. The suspension assembly includes an inner suspension member with the crank axle mounted therein and an outer suspension member surrounding the inner suspension member with a shock absorbing element interposed therebetween. In the preferred embodiment, the shock absorbing element includes a plurality of biasing members.