Abstract: A bicycle frame has a triangular frame structure formed by bracket, seat and head lugs linked together by a seat tube, an upper tube and a lower tube. A chain stay is pivotally connected at a front end to the bracket lug and has a rear end fixed to a rear axle support to which a lower end of a rear fork member is pivotally connected. A triangular link is pivotally connected at a first point adjacent a first apex thereof to the seat lug and also pivotally connected at a second point adjacent a second apex to the upper end of the rear fork member. The triangular link is further pivotally connected at a third point ajacent a third apex to a free end of a cylinder rod of a shock absorbing assembly having a cylinder pivotally connected to the upper tube of the triangular frame structure, whereby the shock absorbing cylinder assembly is operative not only to absorb a shock on the rearwheel but also to provide a "progressive effect" to enhance running performance and suspension and assure a frame rigidity.